Math 11 Home Topic 3 - GSSD · Book 6: Math 11 Home - Angles and Triangles Edited April 2015 . 6.3 Complementary, Supplementary and Vertically Opposite Angles A. Complementary Angles

Math 11 Home

Book 6: Angles and Triangles Teacher Version – Assessments and Answers Included

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Year Overview:

Earning and Spending Money

Home Travel and Transportation

Recreation and Wellness

1. Earning Money 2. Pay Statements

and Deductions 3. Responsible

Spending Habits

4. Data in Your Life 5. Measurement 6. Angles and

Triangles

7. Let’s Travel Project

8. Personal Health and Wellness

9. Puzzles and Games

Topic Overview The intent of this theme is to develop a deeper understanding of the applications of data collection and analysis, measurement, and geometry for the purpose of designing, building, and maintaining a home and yard.

Outcomes

Overlapping Outcomes M11.1 Extend understanding of arithmetic operations to rational numbers to solve problems within the home, money, recreation, and travel themes.

Theme Specific Outcomes M11.5 Demonstrate understanding of angles to solve problems within the home theme. M11.6 Demonstrate understanding of the Pythagorean Theorem to solve problems within the home theme.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Contents Topic Overview.................................................................................................................. 1

Outcomes ....................................................................................................................... 1

Overlapping Outcomes ........................................................................................... 1

Theme Specific Outcomes ....................................................................................... 1

Contents ......................................................................................................................... 2

Glossary of Terms ........................................................................................................... 4

Angles and Triangles ......................................................................................................... 6

Check What You Know ................................................................................................ 7

6.1 Angles ........................................................................................................................... 8

Discuss the Ideas ........................................................................................................... 8

6.1a Practice Your Skills: Measuring and Drawing Angles ...................................... 9

6.1bPractice Your Skills – Identify and Name Angles ............................................. 12

6.1c Practice Your Skills – Drawing Angles ............................................................... 14

6.2 Angle Construction and Bisection ......................................................................... 15

6.2 Practice Your Skills – Constructing Angle Bisectors .......................................... 16

6.3 Complementary, Supplementary and Vertically Opposite Angles .................. 17

A. Complementary Angles ........................................................................................ 17

6.3A Practice Your Skills: Complementary Angles.................................................. 18

B. Supplementary Angles ........................................................................................... 19

6.3B Practice Your Skills: Supplementary Angles .................................................... 20

C. Vertically Opposite Angles ................................................................................... 21

6.3C Practice Your Skills – Vertically Opposite Angles ........................................... 22

6.3 Practice Your Skills - Go Fish or Memory Card Games .................................... 23

6.4 Square Roots and Irrational Numbers .................................................................... 25

6.4 Practice Your Skills – Determining Square Roots ............................................... 26

6.5 The Right Triangle and Pythagorean Theorem .................................................... 27

6.5a Practice Your Skills – Pythagorean Theorem .................................................. 30

6.5b Practice Your Skills – Missing Leg Length in a Right Triangle ......................... 31

6.5c Practice Your Skills – Right Triangle Problem Solving ..................................... 32

Student Evaluation .......................................................................................................... 39

Learning Log .................................................................................................................... 41

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015

6.3 Investigate Activity - Complementary, Supplementary and Vertically Opposite Angles .......................................................................................................... 42

Appendix 1: Complementary, Supplementary and Vertically Opposite Angles ........................................................................................................................................ 43

6.3 Practice Your Skills - Go Fish or Memory Card Games .................................... 44

Appendix 2: Go Fish or Memory Card Games ...................................................... 46

Show What You Know – Project .................................................................................... 61

Answers ............................................................................................................................. 62

Check Your Skills ....................................................................................................... 62

6.1a Practice Your Skills - Measuring and Drawing Angles ............................... 62

6.1b Practice Your Skills – Identify and Name Angles ........................................ 63

6.1c Practice Your Skills – Drawing Angles ........................................................... 64

6.2 Practice Your Skills – Constructing Angle Bisectors ...................................... 65

6.3A Practice Your Skills - Complementary Angles ............................................. 66

6.3B Practice Your Skills - Supplementary Angles ............................................... 67

6.3C Practice Your Skills – Vertically Opposite Angles ....................................... 68

6.5a Practice Your Skills – The Right Triangle and Pythagorean Therem ......... 69

6.5b Practice Your Skills – Missing Leg of a Right Triangle .................................. 70

6.5c Practice Your Skills – Right Triangle Problem Solving .................................. 70

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Glossary of Terms acute angle

an angle that is less than 90 degrees angle bisector

a line passing through the vertex of an angle that cuts it into two equal smaller angles

angles

created whenever two lines of straight surfaces meet complementary angles

two angles that add up to 90 degrees irrational numbers

a real number that cannot be written as a fraction non-perfect squares

a square root that has a root that is not an integer obtuse angle

an angle that is greater than 90 degrees but less than 180 degrees perfect squares

a number that is the square of a whole number protractor

an instrument used to measure angles Pythagorean Theorem

a triangle in which the square of the hypotenuse is equal to the sum of the squares of the other two sides

ray

a portion of a line which starts at a point and goes off in a particular direction to infinity

reflex angle

an angle that is greater than 180 degrees but less than 360 degrees right angle

an angle that is exactly 90 degrees

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 square roots

a number which, when multiplied by itself, results in a given number straight angle

an angle that is exactly 180 degrees supplementary angles

two angles that add up to 180 degrees triangle

a three sided figure created when connecting any three points vertex

the point at which two rays meet to form an angle vertically opposite angles

the angles opposite each other when two lines cross

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Math 11 Home

Angles and Triangles

Angles are created whenever two lines or straight surfaces meet. In our homes, we need to know the size of angles when cutting baseboards, creating rafters, and landscaping our yards.

A triangle is a three sided figure. You can create a triangle by connecting any three points. There is only 1 situation where you cannot make a triangle from 3 points. Can you think of what three points cannot make a triangle?

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Check What You Know

1. Circle the numbers that are perfect squares?

1 2 5 4 8 9 14 16

2. Find the square roots:

a) √25 b) √100 c) √36 d) √1

3. Match the following terms with their definitions.

_____ 1) Ray

_____ 2) Vertex

_____ 3) Acute angle

_____ 4) Obtuse angle

_____ 5) Reflex angle

_____ 6) Straight angle

_____ 7) Right angle

a) an angle that is greater than 90° but less than 180°.

b) an angle that is exactly 180°.

c) an angle that is greater than 180° but less than 360°.

d) an angle that is exactly 90°.

e) an angle that is less than 90°

f) the point at which two rays meet to form an angle

g. a portion of a line which starts at a point and goes off in a particular direction to infinity.

Math skills are embedded into real life situations. In this unit, you will use the following skills:

• Angle terms: ray, vertex

• Angle types: acute, obtuse, reflex, straight and right

• Perfect squares • Square roots

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.1 Angles To measure angles, we can use a protractor. There are different types of protractors, including those that are a full circle and those that are a half circle. Half circle protractors are very common in school.

Discuss the Ideas Brainstorm: “What is an angle?” Jot down all of your ideas. Share your ideas. Consider the following questions: 1. If an angle is a measure of rotation, how many degrees is one rotation?

2. How can you estimate the measure of an angle?

3. How are angles measured?

4. Can you measure a reflex angle?

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.1a Practice Your Skills: Measuring and Drawing Angles Common Angles

1. One of these angles is 30°. Which one do you think it is?



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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 4. Create referent angles of 30°, 45°, 60°, 90°, 180° using a clock face, folding

paper, etc. Sketch an angle of given measure (e.g. 38°) using the referents.

Referent Angle Sketch of Given Measure 30°

38°

45° 51°

60°

66°

90°

95°

180°

192°

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 5. Use a circle to create and label acute, obtuse, right, straight and reflex

angles. a) b)

c) d)

e)

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6.1bPractice Your Skills – Identify and Name Angles Part 1 - Identify Angles: Identify and name types of angles (e.g. acute, obtuse, right, straight and reflex) seen in objects located in your classroom. Angle type Object displaying

Practice: Angle Worksheets www.math-aids.com/Geometry/Angles/

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http://www.math-aids.com/Geometry/Angles/

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Part 2 - Name Angles: Classify each angle as acute, obtuse, right or straight.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.1c Practice Your Skills – Drawing Angles

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.2 Angle Construction and Bisection Materials: Mira, compass, protractor, straight edge

Constructions Angle Bisectors Paper Folding (Informal Construction)

Fold paper at the vertex, making sure that one ray is directly matched over the other.

MIRA (Informal Construction)

Place MIRA on the vertex, through the middle of the angle. Reflect one ray onto the other. Draw in the dotted

line. Compass and Straight Edge (Formal Construction) Note: It is easier to draw the intersecting arcs when the radius of the compass is greater than half of the length of the line segment shown. Note: No measuring is involved in constructions!

Place compass on vertex. Draw an arc of the same length on each ray. Place compass on points where arcs intersect the rays and draw a new arc from each. Draw a line connecting vertex and the new intersection point.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.2 Practice Your Skills – Constructing Angle Bisectors Use any strategy or tool you need to complete the following:

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3 Complementary, Supplementary and Vertically Opposite Angles

A. Complementary Angles Two angles are complementary when they add up to 90 degrees (a right angle). They don’t have to be next to each other, just so long as the total is 90 degrees. For example, 40° and 50° are complementary angles.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3A Practice Your Skills: Complementary Angles

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 B. Supplementary Angles

Two angles are supplementary when they add up to 180 degrees. They don’t have to be next to each other, just so long as they add up to 180 degrees. For example, 40° and 140° are supplementary angles.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3B Practice Your Skills: Supplementary Angles

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C. Vertically Opposite Angles Vertically opposite angles are the angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertically opposite. Notice in the diagram below, the 4 angles are actually two oairs of vertical angles.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3C Practice Your Skills – Vertically Opposite Angles Find the missing vertical angles.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3 Practice Your Skills - Go Fish or Memory Card Games Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, pp.11 - 12 Materials: Cards numbered 0° to 180° plus any extras. These are in Appendix 2. Instructions: • Each group is provided with a set of cards that are to be shuffled. The game

can be played in a variety of ways: 1. Each player is dealt 6 cards. Taking turns, each player asks someone else

if he/she has a particular card. The card that is requested must be one that is a supplement to a card in the player’s hand. If the card is a supplement, he/she must give it to the requester. If not, the player requesting draws one card. If the card is a supplement to a card in the player’s hand, he/she may lay the two cards down. If not, the player keeps the card in his/her hand and play moves to the next player. The game is completed when one player has laid down all of his/her cards as supplementary angles.

2. Each player is dealt 6 cards. The goal of this version is also to collect pairs of angle cards that are supplements, but in this version a player does not request cards from other players. Rather he/she draws a single card at the start of each turn or takes the last previously discarded card. The player ends his/her turn by discarding one card. When a player has all of the angle cards in his/her hand matched as supplements, the game is completed.

3. Spread the cards out face down. Players take turns flipping over two cards. If the cards are supplementary angles, the player removes the two cards and draws again. If they are not supplementary, the cards are flipped back over and the next player starts his/her turn. The game ends after a set period of time or once there are no remaining pairs. The player who has collected the most pairs is the winner.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Adaptations: • Have students write the rules for their favorite version of the game. • Play these games using complementary angles. Remove all cards which

have obtuse and straight angle measures. • The “go fish” version may also be played where rather than asking for a

particular value (40) the person asks for the complement to 50 degrees. • Increase the difficulty level by playing both supplementary and

complementary at the same time. • Once students are familiar with integers, negative angles could be

introduced. • Cards including angles with decimals may also be added to the game (e.g.,

37.5°, 78.6°).

Extension: In any of the versions of the game, students with remaining angle cards could be asked to either construct the angle and its complement and/or supplement or to sketch them.

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Example: To estimate√7.5, visualize the number line and the closest perfect

square on each side of 7.5.

√4 = 2 √9 = 3

√7.5 is closer to 3 than to 2. From the diagram, an approximate value for √7.5 is 2.7. We write √7.5 ≈ 2.7.

6.4 Square Roots and Irrational Numbers Check your understanding of square roots, perfect squares, non-perfect squares and irrational numbers using benchmarks. Knowing perfect squares are helpful when estimating the square roots of non-perfect squares.

Number (Square Root)

Perfect Square (Squared Number)

Number (Square Root)

Perfect Square (Squared Number)

1 1 11 121 2 4 12 144 3 9 13 169 4 16 14 196 5 25 15 225 6 36 16 256 7 49 17 289 8 64 18 324 9 81 19 361

10 100 20 400

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.4 Practice Your Skills – Determining Square Roots Using the benchmark method, determine the approximate value for the following. Between which two consecutive whole numbers is each square root?

1. √12

2. √20

3. √54

4. √95

5. √135

6. Select 2 of your favorite numbers (For example, hockey shirt, house address, birth date, birth year, number of Facebook friends, etc.) With these numbers, use the benchmark method, and determine the approximate value of the square root of each.

a. b.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.5 The Right Triangle and Pythagorean Theorem What is a right angled triangle? A right angled triangle is a triangle that has a right angle (90°) in it.

The little square in the corner tells us that it is a right angled triangle. In a right-angled triangle, we use certain words to describe its parts.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Pythagorean Theorem Over 2000 years ago a Greek Mathematician noticed a special relationship when a triangle has a right angle (90°). When squares are made on each side of the triangle, the biggest square has the exact same area as the other two squares put together.

Interactive: To learn about right triangles, try this site and select right triangles: Triangles http://www.mathsisfun.com/geometry/triangles-interactive.html Interactive: To learn about Pythagoras` Theorem, try this site: Pythagoras http://www.mathsisfun.com/pythagoras.html

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http://www.mathsisfun.com/geometry/triangles-interactive.html

http://www.mathsisfun.com/pythagoras.html

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Pythagorean Theorem is used to find the hypotenuse in the right angles below.

a2 + b2 = c2

1. a = 15, b = 20

2. a = 48, b = 55

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.5a Practice Your Skills – Pythagorean Theorem Find the hypotenuse in the right angles below. 1.

2.

3.

http://www.math-aids.com

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http://www.math-aids.com/

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.5b Practice Your Skills – Missing Leg Length in a Right Triangle Find the missing side of each triangle. Round your answer to the nearest tenth if necessary.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.5c Practice Your Skills – Right Triangle Problem Solving Unknown Side Lengths in Right Triangles Complete the problems. Make sure to draw pictures to help you solve the problems.

1. Tom has a bird named Jerry. Jerry was sitting 5 metres away from the base of a tree. He sees another bird on a branch of a tree 12 metres away. Find the exact distance between Jerry and the other bird.

2. Jack had to paint the wall of his bedroom so he used a ladder. He placed the ladder 10 feet from a wall. The ladder reaches 13 feet up on the wall. Find out how long the ladder is.

3. Fred bought an LCD TV 12 inches long. The diagonal of the LCD TV measures 20 inches. Find the width of the TV.

4. In triangle OPQ, OQ is 17 meters, PQ is 15 meters, find OP.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.6 Right Triangles in Buildings and in Construction Often, when builders want to make sure that they are building something that is square, they use the Pythagorean Theorem. To do this, they check the side lengths and diagonal length of a triangle to see if it satisfies the Pythagorean Theorem. They Pythagorean Theorem is true for right triangles only, so if it works, it means that the angle created is a right angle (90°) Whether it is new construction of a house or a stairway that has seen some time, right triangles and the Pythagorean Theorem also define relationships of distances. Sometimes, distances can’t be determined with a carpenter’s tape, either, because obstacles are in the way or the distances are too large. In these cases, the Pythagorean Theorem has often been of assistance. Example 1: Determine whether the triangle below is a right triangle. If a2 + b2 = c2, then it is a right triangle. a2 + b2 ≟ c2 82 + 242 ≟ 252 64+ 576 ≟ 625 640 ≠ 625 This is not a right triangle.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Example 2: Adam is building a rectangular patio with dimensions of 18 ft x 24 ft. To check if his corners are square, he measures the diagonal which is 30 ft. Are his corners square? (If his corners are “square”, it means that the angle between the two sides a right angle). Justify your answer. a2 + b2 ≟ c2

182 + 242 ≟ 302

324 + 576 ≟ 900 900 = 900 Yes, his corners are square because his two sides and the diagonal make a right triangle.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.6 Practice your Skills – Right Triangles in Building and Construction

1. Determine whether the triangle below is a right triangle.

2. Each set of measurements below represents the side lengths of a triangle. Identify which triangles are right triangles. How do you know?

a) 3 cm, 4 cm, 6 cm b) 7 m, 24 m, 25 m c) 6 cm, 8 cm, 10 cm d) 1 m, 2 m, 5 m e) 2 m, 3 m, 12 m

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3. Joe is building a frame for his window. The frame is 88 cm wide and 105 cm tall. He measures the diagonal of his frame and finds that it is 137 cm. Is the frame a rectangle? Justify your answer.

4. Danielle is laying a foundation for a farm shed with dimensions 10 m by 6 m. To check that the foundation is square, Danielle measures a diagonal. How long should the diagonal be? Give your answer to one decimal place.

5. Juan is building a doorframe with dimensions of 1 m by 2 m. He measures the diagonal to be 2.7 m. Is the angle between the two sides a right angle? Justify your answer.

6. Ben is laying a plywood floor in his cabin. The floor is rectangular with side lengths 9 m and 12 m. He measures the diagonal of the floor as 15 m. Is the angle between the two sides a right angle? Justify your answer.

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7. The photograph shows stairs going up a rock wall in a diagonal pattern. If the set of stairs is 9.4 m long and the horizontal distance that a person travels going up the stairs is 7.5 m, what is the height of the stairs? Give your answer in metres to one decimal place.

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8. In the photograph of the house under construction, a long 2 by 4 diagonal brace is shown near the centre of the picture. If the framers of the house know that the height of the wall is going to be 2.44 m and they want to brace the wall at right angles to the floor, how far from the wall should they place the bottom of the 3.66 m diagonal brace? Give your answer in metres to two decimal places.

In the same picture above, you can see a gable end of the roof. If the width of the roof is 4.28 m and the height of the gable end is 1.22 m, what is going to be the length of each side of the roof truss? Give your answer in metres to two decimal places.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Student Evaluation

Proficient Level Criteria IE D G P E

M11.1 Extend understanding of arithmetic operations to rational numbers to solve problems within the home, money, recreation, and travel themes.

d. I can round decimals.

f. I can determine if my answer is reasonable.

M11.5 [WA 10.9] Demonstrate understanding of angles to solve problems within the home theme.

a. I can use appropriate referents for a variety of angles to estimate angle measurements (e.g., a corner of a sheet of paper is 90° so ½ of a corner is 45°).

b. I can measure angles in different orientations

c. I can be replicate and explain how angles can be drawn using a variety of tools. (e.g., Mira, protractor)

d. I can identify, classify, and sketch angles of various measures, including acute, right, straight, obtuse, and reflex angles.

e./f. I can bisect angles and explain what bisect means.

g. I can identify adjacent angles that are complementary, supplementary, or neither, and explain why.

h. I can solve problems involving complementary and supplementary angles.

i. I can identify vertically opposite angles and solve situational problems.

Insufficient Evidence (IE)

Developing (D) Growing (G) Proficient (P) Exceptional (E)

Student has not demonstrated the criteria below.

Student has rarely demonstrated the criteria below.

Student has inconsistently demonstrated the criteria below.

Student has consistently demonstrated the criteria below.

Student has consistently demonstrated the criteria below. In addition they have shown their understanding in novel situations or at a higher level of thinking than what is expected by the criteria.

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Proficient Level Criteria IE D G P E

M11.6 [WA 10.6] Demonstrate understanding of the Pythagorean Theorem to solve problems within the home theme.

a. I can explain the meaning, role, and use of the Pythagorean Theorem, with examples and non-examples.

b. I can apply the Pythagorean 3:4:5 ratios to determine if angles are square (right angles) in home construction contexts.

c. Apply the Pythagorean Theorem to solve for a missing side.

d. Estimate the values of irrational numbers using a table of perfect squares, multiplication chart, or a number line and show appropriate rounding of irrational numbers.

e. I can observe and analyze the use of Pythagorean lengths of diagonals of various building structures (eg. Trusses, frames, door jambs, window casings).

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Learning Log Date Starting Point Ending Point

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3 Investigate Activity - Complementary, Supplementary and Vertically Opposite Angles Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, p. 11 Materials: Brads Straight angle (2) and right angle templates (made of cardstock) Paper strip Protractor Complementary and supplementary angles come in pairs and as the measure of one angle of the pair increases, the other decreases. The purpose of this activity is to physically manipulate angles to develop a better understanding of complementary and supplementary angles. You will also develop a better understanding of vertically opposite angles. Investigate: Using the right angle template, attach the ray template to the vertex of the angle using a brad, and then move the ray up and down, measuring the resulting angles with a protractor. Record the measures of angles 1 and 2 in the table below and determine the relationship. ∠1 ∠2 Using the straight angle template (Appendix 1), attach the ray template to the center of the line using a brad, and then move the ray up and down, measuring the resulting angles with a protractor. Record the measures of angles 1 and 2 in the table below and determine the relationship. ∠1 ∠2 Using two straight angle templates (Appendix 1), attach them in the center of each line using a brad, creating an X. Measure the angles with a protractor. Record the measures of angles 1 and 2 in the table below and determine the relationship. ∠1 ∠2

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Appendix 1: Complementary, Supplementary and Vertically Opposite Angles

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3 Practice Your Skills - Go Fish or Memory Card Games Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, pp.11 - 12 Materials: Cards numbered 0° to 180° plus any extras. These are in Appendix 2. Instructions: • Each group is provided with a set of cards that are to be shuffled. The game

can be played in a variety of ways: 4. Each player is dealt 6 cards. Taking turns, each player asks someone else

if he/she has a particular card. The card that is requested must be one that is a supplement to a card in the player’s hand. If the card is a supplement, he/she must give it to the requester. If not, the player requesting draws one card. If the card is a supplement to a card in the player’s hand, he/she may lay the two cards down. If not, the player keeps the card in his/her hand and play moves to the next player. The game is completed when one player has laid down all of his/her cards as supplementary angles.

5. Each player is dealt 6 cards. The goal of this version is also to collect pairs of angle cards that are supplements, but in this version a player does not request cards from other players. Rather he/she draws a single card at the start of each turn or takes the last previously discarded card. The player ends his/her turn by discarding one card. When a player has all of the angle cards in his/her hand matched as supplements, the game is completed.

6. Spread the cards out face down. Players take turns flipping over two cards. If the cards are supplementary angles, the player removes the two cards and draws again. If they are not supplementary, the cards are flipped back over and the next player starts his/her turn. The game ends after a set period of time or once there are no remaining pairs. The player who has collected the most pairs is the winner.

44

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Adaptations: • Have students write the rules for their favorite version of the game. • Play these games using complementary angles. Remove all cards which

have obtuse and straight angle measures. • The “go fish” version may also be played where rather than asking for a

particular value (40) the person asks for the complement to 50 degrees. • Increase the difficulty level by playing both supplementary and

complementary at the same time. • Once students are familiar with integers, negative angles could be

introduced. • Cards including angles with decimals may also be added to the game (e.g.,

37.5°, 78.6°).

Extension: In any of the versions of the game, students with remaining angle cards could be asked to either construct the angle and its complement and/or supplement or to sketch them.

45

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Appendix 2: Go Fish or Memory Card Games

0° 5° 10°

15° 20° 25°

30° 35° 40°

46


45° 50° 55°

60° 65° 70°

75° 80° 85°

47


90° 95° 100°

105° 110° 115°

120° 125° 130°

48


135° 140° 145°

150° 155° 160°

165° 170° 175°

49


180° FREE FREE

15° 20° 25°

30° 35° 40°

50


45° 50° 55°

60° 65° 70°

75° 80° 85°

51


90° 95° 100°

105° 110° 115°

120° 125° 130°

52


135° 140° 145°

150° 155° 160°

165° 170° 175°

53


180° FREE FREE

0° 5° 10°

0° 5° 10°

54


15° 20° 25°

180° FREE FREE

30° 35° 40°

55


45° 50° 55°

DRAW 2 DRAW 2 DRAW 2

60° 65° 70°

56


75° 80° 85°

90° 95° 100°

105° 110° 115°

57


120° 125° 130°

135° 140° 145°

150° 155° 160°

58


165° 170° 175°

59


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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Show What You Know – Project Angles in Construction Consider the design of a shed, dog house, ice fishing shack, etc.

Describe the cutting angles for framing a window with casing or a room with baseboards where mitre cuts are required. Resources

Draw a Floor Plan MathWorks 10 (2010). p. 105

Basic Carpentry Framing Tips http://www.carpentry-pro-framer.com/index.html

J & H Builders Window Measure Information Form: http://www.jhbuilders.com/common/pdf/window_measure_form042910.pdf

J & H Builders Door Measure Information Form: http://www.jhbuilders.com/common/pdf/door_measure_form042910.pdf

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http://www.carpentry-pro-framer.com/index.html

http://www.jhbuilders.com/common/pdf/window_measure_form042910.pdf

http://www.jhbuilders.com/common/pdf/door_measure_form042910.pdf

Book 6: Math 11 Home - Angles and Triangles Edited April 2015 Answers

Check Your Skills 1. 1, 4, 9, 16 2. a) 5 b) 10 c) 6 d) 1 3. 1)g 2)f 3)e 4)a 5)c 6)b 7)d

6.1a Practice Your Skills - Measuring and Drawing Angles Answers: 1. A 2. D 3. B 4. Answers will vary. Answers will vary.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.1b Practice Your Skills – Identify and Name Angles Part 1 Table – answers may vary. Part 2:

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.1c Practice Your Skills – Drawing Angles

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.2 Practice Your Skills – Constructing Angle Bisectors

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3A Practice Your Skills - Complementary Angles

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3B Practice Your Skills - Supplementary Angles

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.3C Practice Your Skills – Vertically Opposite Angles

6.4 Practice Your Skills – Determining Square Roots

1. Between 3-4; 3.46 2. Between 4-5; 4.47 3. Between 7-8; 7.35 4. Between 9-10; 9.75 5. Between 11-12; 11.62 6. a) answers may vary

b) answers may vary

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.5a Practice Your Skills – The Right Triangle and Pythagorean Therem 1.

2.

3.

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Book 6: Math 11 Home - Angles and Triangles Edited April 2015 6.5b Practice Your Skills – Missing Leg of a Right Triangle

6.5c Practice Your Skills – Right Triangle Problem Solving 1. 13 metres 2. 16 feet 3. 16 inches 4. OP = 8

6.6 Practice your Skills – Right Triangles in Building and Construction

1. Yes 169=169 2. a) No, 25 ≠ 36

b) Yes, 625 = 625 c) Yes, 100 = 100 d) Yes, 5 = 5 e) No, 13 ≠ 12

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3. Yes, 18 769 = 18 769 So, the frame is a rectangle since its corners form right angles.

4. About 11.7m 5. No, about 2.2 m ≠ 2.7 m 6. yes, 225 = 225 7. About 12.0 m 8. 1.22 m 9. 2.46 m

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Math 11 Home Topic 3 - GSSD · Book 6: Math 11 Home - Angles and Triangles Edited April 2015 . 6.3 Complementary, Supplementary and Vertically Opposite Angles A. Complementary Angles

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