CC BGE TE Extra Practice 13-2amhs.ccsdschools.com/UserFiles/Servers/Server_2856713/File/Staff... · See Additional Answers. EPS3 Extra Practice Applications Practice Athletics Use

Extra Practice

Extra Practice Skills Practice

Name each of the following.

1. two points 2. two lines

3. two planes 4. a point on IH

5. a line that contains L and J

6. a plane that contains L, K, and H

Draw and label each of the following.

7. a ray with endpoint A that passes through B

8. a line PQ that intersects plane

Find each length.

9. MN 10. MO

11. Segments that have the same length are ? .

12. Construct a segment congruent to AB. Then construct the midpoint M.

13. M is the midpoint of PR , PM 2x 5, and MR 4x 7. Solve for x and find PR.

Z is in the interior of WXY. Find each of the following.

14. m WXY if WXZ 23° and m ZXY 51°

15. m WXZ if m WXY 44° and m ZXY 20°

EH bisects DEF. Find each of the following.

16. m DEH if m DEH 10z 2 ° and m HEF 6z 10 °

17. m DEF if m DEH 9x 3 ° and m HEF 5x 11 °

18. A ? is formed by two opposite rays and measures ? °.

19. There are ? ° in a circle.

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

20. AOB and DOE 21. AOE and DOE

22. COE and EOA 23. AOB and BOD

24. Name a pair of vertical angles.

Given m A 41.7° and m B 24.2 x °, find the measure of each of the following.

25. complement of A 26. supplement of A 27. supplement of B

Lesson

1-1

Lesson

1-2

Lesson

1-3

Lesson

1-4

,

8 14

Check students’ constructions.

x 6, PR 34

74°

24°

28°

42°

straight ; 180

360

20. not adj.

21. only adj.

22. adj. and a lin. pair

23. only adj.Possible answers: AOE and BOC

48.3° 138.3°27. 155.8 x °

1–6. Possible answers:

7–8. See Additional Answers.

LJ

H, I JK , IH

H

EPS2

Chapter 1 Find the perimeter and area of each figure.

28. 29. 30.

Find the circumference and area of each circle. Give your answer to the nearest hundredth.

31. 32. 33.

34. The formula to find the midpoint M of AB with endpoints A x 1 , y 1 and B x 2 , y 2 is ? .

Find the coordinates of the midpoint of each segment.

35. WX with endpoints W 4, 1 and X 2, 9

36. YZ with midpoints Y 4, 8 and Z 1, 4

37. M is the midpoint of RS . R has coordinates 7, 3 , and M has coordinates 1, 1 . Find the coordinates of S.

Find the length of the given segments and determine if they are congruent.

38. VW and PQ

39. RS and TU

2

4

2

2

Identify each transformation. Then use arrow notation to describe the transformation.

40. 41.

42. A figure has vertices at 1, 1 , 2, 4 , and 5, 3 . After a transformation, the image of

the figure has vertices at 3, 2 , 2, 1 , and 1, 0 . Draw the preimage and image.

Then describe the transformation.

43. A figure has vertices at 5, 5 , 2, 6 , 1, 5 , and 2, 4 . After a transformation, the

image of the figure has vertices at 5, 5 , 6, 8 , 5, 9 , and 4, 8 . Draw the preimage

and image. Then describe the transformation.

44. The coordinates of the vertices of quadrilateral DEFG are 3, 0 , 2, 3 , 3, 2 , and

2, 1 . Find the coordinates for the image of rectangle DEFG after the translation

x, y x, y . Draw the preimage and image. Then describe the transformation.

Lesson

1-5

Lesson

1-6

Lesson

1-7

1, 5

9, 5

38. VW 8 2 ; PQ 3 5 ; no

39. RS TU 34 ; yes

rotation; GHI G H I

36. 1 1 _

2 , 2



See Additional Answers.

EPS3

Extra Practice Applications Practice

Athletics Use the following information for Exercises 1–3.

During gym class, a teacher notices the following. Decide if each resembles a point, segment, ray, or line. (Lesson 1-1)

1. Kyle starts running in a straight line. Suppose he does not stop running.

2. Agnes runs a quarter-mile in a straight line.

3. Jimmy stands perfectly still.

Travel Use the following information for Exercises 4–6.

The Perez family is driving from Austin, Texas, to Dallas, Texas. The city of Waco is the approximate midpoint between these two cities. It is 102 miles from Austin to Waco. (Lesson 1-2)

4. What is the total distance from Austin to Dallas?

5. The approximate midpoint from Waco to Dallas is Milford. What is the distance from Austin to Milford?

6. The Perez family averages 64 miles per hour. About how long will the entire drive take?

Probability Use the following information for Exercises 7 and 8.

In a carnival game, each contestant spins the wheel and wins the prize indicated by the color. (Lesson 1-3)

7. Using a protractor, measure each angle on the wheel.

8. Since there are 360° in a circle, the probability of the wheel landing on a given color is the number of degrees in the angle divided by 360°. Find the probability of the wheel landing on each prize. Express your answer as a fraction in lowest terms.

9. Entomology Because the insect is symmetrical, ∠1 ! ∠4 and ∠2 ! ∠3. Also, ∠1 and ∠2 are complementary, and ∠3 and ∠4 are complementary. If m∠1 = 48.5°, find m∠2, m∠3, and m∠4. (Lesson 1-4)

Architecture Use the following information for Exercises 10 and 11.

The bricks used to make a building are one-fourth as tall as they are wide, and the bricks are 2.25 inches tall. (Lesson 1-5)

10. What is the area of the largest face of each brick?

11. A certain exterior wall is 33 bricks long and 20 bricks tall. What is the area of the wall in square inches?

12. Sports A football coach has his team run sprints diagonally across a football field. If the field is 120 yards long and 160 feet wide, what is the distance they run? Write your answer to the nearest hundredth of a foot. (Lesson 1-6)

13. Crafts The picture below shows half of a stenciled design. The full design should resemble a sun. Name two transformations that can be performed on the image so that the image and its preimage form a complete picture. Be as specific as possible, referring to L and P. (Lesson 1-7)

L

P

ray

seg.pt.

204 mi

153 mi

approximately 3 h 11 min

m∠2 = m∠3 = 41.5°; m∠4 = 48.5°

20.25 in 2

13,365 in 2

393.95 ft

reflection across L, rotation of 180° about P


EPA2

Chapter 1

Extra Practice

EPCH1

Extra Practice


Find the next item in each pattern.

1. 3, 7, 11, 15, … 2. 3, 6, 12, 24, …

3. Complete the conjecture “The product of two negative numbers is ? .”

4. Show that the conjecture “The quotient of two integers is an integer” is false by finding a counterexample.

Identify the hypothesis and conclusion of each conditional.

5. A number is divisible by 10 if it ends in zero.

6. If the temperature reaches 100° F, it will rain.

Write a conditional statement from each of the following.

7. Perpendicular lines intersect to form 90° angles. 8.

Track

Athletics 9. The sum of two supplementary angles is 180°.

Determine if each conditional is true. If false,give a counterexample.

10. If a figure has four sides, then it is a square.

11. If x 3 , then 5x 15 .

12. Does the conclusion use inductive or deductivereasoning? To rent a boat, you must take a boatingsafety course. Jason rented a boat, so Jessicaconcludes that he has taken a boating safety course.

13. Determine if the conjecture is valid by the Law of Detachment.Given: If a student is in tenth grade, then the student may participate in student council. Eric is a tenth-grader.Conjecture: Eric may participate in student council.

14. Determine if the conjecture is valid by the Law of Syllogism.Given: If a triangle is isosceles, then it has two congruent sides. If a triangle has two congruent angles, then it has two congruent sides.Conjecture: If a triangle is isosceles, then it has two congruent angles.

15. Draw a conclusion from the given information.Given: If the sum of the angles of a polygon is 360°, then it is a quadrilateral. If a polygon is a quadrilateral, then it has four sides. The sum of the angles of polygon R is 360°.

16. Write the conditional statement and converse within the biconditional “A triangle is equilateral if and only if it has three congruent sides.”

17. For the conditional “If a triangle is scalene, then its sides have different lengths,” write the converse and a biconditional statement.

18. Determine if the biconditional “n 3 1 n 4” is true. If false, give a counterexample.

Write each definition as a biconditional.

19. A parallelogram is a quadrilateral with two pairs of parallel sides.

20. Congruent angles have equal measures.

Lesson

2-1

Lesson

2-2

Lesson

2-3

Lesson

2-4

19 -48

positive

3 ÷ 2 = 1.5

H: A number ends in a zero. C: A number is divisible by 10.

H: The temperature reaches 100° F. C: It will rain.

If 2 lines are ⊥, then they intersect to form 90° #.

If 2 # are supp., then their sum is 180°.

If a student is on the track team, then the student is in athletics.

F; a parallelogram has 4 sides but is not a square.

T

deductive

valid

invalid

Polygon R has 4 sides.

T

A quad. is a parallelogram if and only if it has 2 pairs of parallel sides.

2 # are � if and only if they have = measures.


EPS4

Chapter 2 Solve each equation. Write a justification for each step.

21. 2x 3 9 22. x 2

_ 5

3

Write a justification for each step.

23. AC AB BC 9x 5 3x 6 5x 2

+ +

-

9x 5 8x 8

x 5 8

x 13

24. Fill in the blanks to complete the two-column proof.

Given: Prove: Proof:

Statements Reasons

1. a. ?

2. b. ?

c. ?

3.

1. Given

2. Adjacent angles that form a right

angle are complementary.

3. d. ?

25. Use the given plan to write a two-column proof of the Transitive Property of Congruence.

Given: Prove: Plan: Use the definition of congruentsegments to write the given congruence statements as statements of equality. Then use the Transitive Property of Equality to show that So by the definition of congruent segments.

26. Use the given two-column proof to write a flowchart proof.

Given: 2 3 Prove: m 1 m 4Proof:

Statements Reasons

1. 2 3

2. 1 and 2 are supplementary.

3 and 4 are supplementary.

3.

4. m m

1. Given

2. Lin. Pair Thm.

3. Supps. Thm.

4. Def. of

27. Use the given two-column proof to write a paragraph proof.

Given: 1 3 Prove: 4 5Proof:

Statements Reasons

1.

2.

3.

4.

1. Given

2. Vert. Thm.

3. Trans. Prop. of

4. Trans. Prop. of

Lesson

2-5

Lesson

2-6

Lesson

2-7

x + 2 _

5 = 3 (Given); x + 2 = 15

(Mult. Prop. of =); x = 13

(Subtr. Prop. of =)

Seg. Add. Post.; Subst.; Simplify; Subtr. Prop. of =; Add. Prop. of =

� Comps. Thm.

24a. ∠HMK and ∠JML are rt. $.

b. ∠1 and ∠2 are comp.

c. ∠2 and ∠3 are comp.



It is given that ∠1 � ∠3. By the Vert. $ Thm., ∠1 � ∠4 and ∠3 � ∠5. By the Trans. Prop. of �, ∠1 � ∠5. Similarly, ∠4 � ∠5.

EPS5


1. Health Mike collected the following data about the heights of twelve students in his tenth-grade class. Use the table to make a conjecture about the heights of boys and girls in the tenth grade. (Lesson 2-1)

Height (in.) of Tenth-Grade Students

Boys 70 71 68 67 70 67

Girls 67 64 64 65 68 66

2. Government Voter Turnout

Year Voters

1996 12,530

1998 8,750

2000 15,210

2002 7,370

2004 14,380

Presidential elections are held every four years. Elections for senators are held every two years. So in years not divisible by 4, only Senate seats are up for election. The table shows voter turnout for a small town during recent election years. Make a conjecture based on the data. (Lesson 2-1)

3. Biology Write the converse, inverse, and contrapositive of the conditional statement “If an animal is a fish, then it swims in salt water.” Find the truth value of each. (Lesson 2-2)

4. Gardening Write the converse, inverse, and contrapositive of the conditional statement “If a plant is watered, then it will grow.” Find the truth value of each. (Lesson 2-2)

5. Sports Determine if the conjecture is valid by the Law of Detachment. (Lesson 2-3)

Given: If you participate in a triathlon, then you run, swim, and bike. Margie runs, swims, and bikes.

Conjecture: Margie participates in a triathlon.

6. Health Students are required to have certain immunizations before attending school to prevent the spread of disease. Write the conditional statement and converse within the biconditional “Students can attend public school if and only if they have the required immunizations.” (Lesson 2-4)

7. Weather Hurricanes are assigned category numbers to describe the amount of flooding and wind damage they are likely to cause. Write the statement “If a hurricane has sustained winds of more than 155 miles per hour, then it is Category 5” as a biconditional statement. (Lesson 2-4)

8. Athletics The equation c = 5w + 25 relates the number of workouts w to the cost c of a weight training group. If Matthew plans to spend $200 on weight training, how many workouts can he participate in? Solve the equation for w and justify each step.(Lesson 2-5)

9. Nutrition Rick has allotted himself 200 Calories for his evening snack, which consists of a glass of milk and crackers. A glass of milk has 110 Calories, and each cracker has 15 Calories. The equation s = 110 + 15c relates the number of crackers c to the total number of Calories s in Rick’s evening snack. How many crackers can Rick have? Solve the equation for c and justify each step.(Lesson 2-5)

10. Travel On a city map, the library, post office, and police station are collinear points in that order. The distance from the library to the post office is 2.3 miles. The distance from the post office to the police station is 5.1 miles. Which theorem can you use to conclude that the distance from the library to the police station is 7.4 miles? (Lesson 2-6)

11. Recreation Kyle is making a kite from the pattern below by cutting four triangles from different pieces of material. Write a paragraph proof to show that m∠3 = 90°. (Lesson 2-7)

2 1

3 4

Given: ∠1 # ∠2Prove: m∠3 = 90°

invalid

Seg. Add. Post.









11. It is given that ∠1 � ∠2. By the Lin. Pair Thm., ∠1 and ∠2 are supplementary. By Thm. 2-7-3, ∠1 and ∠2 are rt. !. So m∠1 = 90°. By the Vert. ∠s Thm., ∠1 � ∠3, so m∠1 = m∠3 by the def. of � !. By subst., m∠3 = 90°.

EPA3

Chapter 2

Extra Practice

EPCH2

Extra Practice


Identify each of the following.

1. a pair of parallel segments

2. a pair of perpendicular segments

3. a pair of skew segments

Identify the transversal and classify each angle pair.

4. 5 and 3

5. 2 and 4

6. 5 and 1

Find each angle measure.

7. m XYZ

-

+

8. m KJH

9. m ABC

+

10. m LMN

+

+

11. m PQR

+

12. m TUV

+

-

Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ ‖ m.

13. 2 4

14. m 8 5x 36, m 6 11x 12, x 4

Use the theorems and given information to show that p ‖ q.

15. 1 8

16. m 2 9x 31, m 3 6x 14, x 9

17. Write a two-column proof.

Given: 1 and 5 are supplementary. Prove: ℓ m

Lesson

3-1

Lesson

3-2

Lesson

3-3

−−

JK and −−

HL

−−

JK and −−

HJ

Possible answer: −−

JK and −−

HQ

q, alt. int.

r, corr.

p, alt. ext.

41°

63°

85°

125°

98°

120°

∠2 � ∠4, so ℓ ‖ m by the Conv. of Corr. & Post.

∠1 � ∠8, so p ‖ q by the Conv. of Alt. Ext. & Thm.



EPS6

Chapter 318. Name the shortest segment from point A to BE .

19. Write and solve an inequality for x. +

Solve for x and y in each diagram.

20.

-

21. +


Given: ℓ p, m p Prove: ℓ m

Use the slope formula to determine the slope of each line.

23. FG

-

-

24. HJ

-

-

Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither.

25. AB and CD for A 4, 7 , B 3, 2 , C 3, 4 , D 2, 3

26. EF and GH for E 2, 4 , F 3, 1 , G 1, 2 , H 4, 5

27. JK and LM for J 3, 3 , K 4, 2 , L 4, 2 , M 0, 4

Write the equation of each line in the given form.

28. the line with slope 2 _ 3

through 3, 1 in point-slope form

29. the line through 2, 2 and 4, 1 in slope-intercept form

30. the line with x-intercept 3 and y-intercept 4 in slope-intercept form

Graph each line.

31. y 3 _ 4

x 2 32. y 4 3 x 2

33. y 2 34. x 1

Determine whether the lines are parallel, intersect, or coincide.

35. y 4x 2, 4x y 1 36. y 1 _ 2

x 3, 2y x 6

37. 2x 5y 1, 5x 2y 1 38. 2x y 5, 2x y 5

Lesson

3-4

Lesson

3-5

Lesson

3-6

−−

AC

3x + 5 > 9, x > 4 _

3

x = 18, y = 18

x = 10, y = 15

1 0

25–27. For graphs, see Additional Answers.

perpendicular

parallel

neither


y = 4 _

3 x + 4

y = - 1 _

2 x + 1

y + 1 = - 2

_ 3

(x - 3)


parallel

intersect

coincide

intersect

EPS7


1. Recreation A scuba diver leaves a flag on the surface of the water to alert boaters of his location. Describe two parallel lines and a transversal in the flag. (Lesson 3-1)

2. Carpentry In the stairs shown, the horizontal treads and the vertical risers are all parallel. m∠1 = (14x + 6) ° and m∠2 = (19x - 24) °. Find x. (Lesson 3-2)

3. Transportation The train tracks shown cross the street lanes. The lanes of the street are parallel. Find x in the diagram. (Lesson 3 -3)

+

4. Sports At a track meet, the starting blocks are placed along a line that is a transversal to the lanes. m∠1 = 12x - 8, m∠2 = 8x + 12, and x = 5. Show that the lines between the lanes are parallel. (Lesson 3-3)

5. Transportation The railroad ties in the diagram are all parallel. m∠1 = 19x - 5 and m∠ 2 = 4x + 5y. Find x and y so that the ties are all perpendicular to the tracks. (Lesson 3-4)

6. Art The sides of a picture frame are cut so that the opposite sides of the frame are parallel and the consecutive sides are perpendicular. Find the values of x and y in the diagram. (Lesson 3-4)

+ +

7. Recreation At 1:00 P.M., a boat on a river passes a point that is 3 miles from a lodge. At 5:30 P.M., the boat passes a point that is 8 miles from the lodge. Graph the line that represents the boat’s distance from the lodge. Find and interpret the slope of the line. (Lesson 3-5)

8. Sports A marathon runner runs 10 miles by 3:00 P.M. and 25 miles by 4:30 P.M. Graph the line that represents her distance run. Find and interpret the slope of the line. (Lesson 3-5)

9. Business A cab company charges $8 per ride plus $0.25 per mile. Another cab company charges $5 per ride plus $0.35 per mile. For how many miles will two cab rides cost the same amount? (Lesson 3-6)

10. Food A pizza parlor is catering a schoolevent. Pete’s Pizza charges $85 for the first20 students and $5 for each additional student. Polly’s Pizza charges $125 for the first20 students and $3 for each additional student. For how many students will the pizza parlors cost the same? (Lesson 3-6)

Possible answer: The top and the bottom of the flag are ‖. The white stripe is a transv.

x = 6

x = 10

x = 5, y = 14

x = 5, y = 25

30 miles

40 students




EPA4

Chapter 3

Extra Practice

EPCH3

Extra Practice


Apply the transformation M to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation.

1. M: (x, y) (–x, y) 2. M: (x, y) (x – 2, y + 2)

A(4, 5), B(1, 3), C(2, 6) P(–3, 2), Q(5, 0), R(4, –2)

Determine whether the polygons with the given vertices are congruent. Support your answer by describing a transformation.

3. X(1, –3), Y(0, 2), Z(–1, 4) and M(3, –9), N(0, 6), P(–3, 12)

Classify each triangle by its angle measures.

4. ABC

5. BCD

Classify each triangle by its side lengths.

6. EFG

7. FGH

8. EFH

9. Find the side lengths of JKL.

+

+

-

The measure of one of the acute angles of a right triangle is given. What is the measure of the other acute angle?

10. 38° 11. 27.6°


12. m A -

+

13. m J and m P

-

Given: △GHI � △JKL. Identify the congruent corresponding parts.

14. GH ? 15. JL ? 16. K ?

Given: △LMN � △PQN. Find each value.

17. x

+

-

18. m LMN

Use SSS to explain why the triangles in each pair are congruent.

19. QRS QRT 20. UVW WXU

Show that the triangles are congruent for the given value of the variable.

21. XYZ ABC, 22. DEF GFE, x 4 y 8

-

-

-

-

+

-

Lesson

4-1

Lesson

4-2

Lesson

4-3

Lesson

4-4

Lesson

4-5

equiangular

rt.

equil.

isosc.

scalene

JL = 31, KL = 31, JK = 32

52° 62.4°

65° 25°

−−

JK −−

GI ∠H

7.5

18°

19–22. See Additional Answers

3. No, the triangles are not congruent because triangle XYZ can be mapped to triangle

MNP by a dilation with a scale factor of 3 and a center of (0, 0).

2. P(–5, 4), Q(3, 2), R(2, 0)

This is a translation 2 units left and 2 units up.

1. A'(–4, 5), B'(–1, 3), C'(–2, 6) This is a reflection across the y-axis.

EPS8

Chapter 4 Determine if you can use ASA to prove the triangles congruent. Explain.

23. ACB ACD 24. EFG HGF

Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.

25. ABC EDC 26. FGH FJH

27. Given: MN LP , 28. Given: 1 6, 4 6N L 1 3, AB AE

Prove: ML PN Prove: ACD is isosceles.

29. Given: ABC with vertices A 2, 4 , B 3, 1 , C 5, 2 and DEF with vertices

D 4, 2 , E 1, 3 , F 2, 5

Prove: BAC EDF

Position each figure in the coordinate plane.

30. a rectangle with length 7 units and width 3 units 31. a square with side length 3a

Write a coordinate proof.

32. Given: Right GHI has coordinates G 0, 0 , H 0, 4 , and I 6, 0 .

J is the midpoint of GH , and K is the midpoint of GI .

Prove: The area of GJK is 1 __ 4 the area of GHI.

Assign coordinates to each vertex and write a coordinate proof.

33. Given: A is the midpoint of XW in rectangle WXYZ.

B is the midpoint of YZ .

Prove: AB XY


34. m X 35. m A

+ -

Find each value.

36. x

+

37. y

-

+

38. Given: XYZ is isosceles.A is the midpoint of XZ . XY YZ

Prove: YAZ is isosceles.

Lesson

4-6

Lesson

4-7

Lesson

4-8

Lesson

4-9

-

-

64° 20°

10 4


See Additional Answers

EPS9


1. Crafts On a coordinate plane, patterns for two pieces of stained glass have coordinates A(4, 1), B(3, 5), C(1, 2) and D(1, 3), E(5, 2), F(2, 0). Prove that the patterns are congruent. (Lesson 4-1)

2. Camping Three poles are used to create the frame for a tent. The front of the tent is an isosceles triangle with AB BC . The length of the base is 1.5 times the length of the sides. The perimeter of the triangle is 21 ft. Find each side length. (Lesson 4-2)

3. Geography The universities in Durham, Chapel Hill, and Raleigh, North Carolina form what is known as the Research Triangle. Use the map to find the measure of the angle whose vertex is at Durham. (Lesson 4-3)

4. Business Oil derricks are used as supports for oil drilling equipment. Use the diagram to prove the following. (Lesson 4-4)

Given: AB HG , HB AG GAB BHG, AGB HBG

Prove: AGB HBG

5. Sports A kite is made up of two pairs of congruent triangles. Use SAS to explain why

ABD CBD. (Lesson 4-5)

6. Recreation A student is estimating the height of a water slide. From a certain distance, the angle from where he is standing to a point on the highest part of the slide is 35°. From a distance 200 m closer, the same angle is 45°. Which postulate or theorem can be used to show that the triangle with the point at the top of the slide as one vertex, and the points where the measurements were taken as the other vertices, is uniquely determined? (Lesson 4-6)

7. Surveying To find the distance AB across a lake, first locate point C. Then measure the distance from C to B. Locate point D the same distance from C as B, but in the opposite direction. Then measure the distance from C to A and locate point E in a similar manner. What is the distance AB across the lake? (Lesson 4-7)

8. The first step in creating a Sierpinski triangle is to connect the midpoints of the sides of a triangle as shown. (Lesson 4-8)

Given: Equilateral ABC, D is the midpoint

of AB , E is the midpoint of AC , and F is

the midpoint of BC .

Prove: The area of DEF is 1 __ 4 the area of ABC.

9. Recreation A boat is sailing parallel to the coastline along XY . When the boat is at X, the measure of the angle from the lighthouse W to the boat is 30°. After the boat has traveled 5 miles to Y, the angle from the lighthouse to the boat is 60°. How can you find WY? (Lesson 4-9)

AB = 6, BC = 6, AC = 9

88°

135 yd

9. Since the boat is parallel to the coastline,

−− WZ ‖

−− YX .

So ∠ZWX � ∠WXY. Since m∠YWZ = 60° and m∠XWZ = 30°, by subtr., m∠YWX = 30°. Therefore △WYX is isosc. and

−− WY �

−− YX .

Thus WY = 5.





AAS or ASAEPA5

Chapter 4

Extra Practice

EPCH4

Extra Practice


Find each measure.

1. CD 2. HG 3. JM

4. m SRT, given m SRU 126° 5. PQ 6. m WXV

7. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A 1, 4 and B 5, 2 .

DG , EG , and FG are the perpendicular bisectors of ABC. Find each length.

8. BG 9. AG

Find the circumcenter of a triangle with the given vertices.

10. H 5, 0 , J 0, 3 , K 0, 0 11. L 0, 0 , M 2, 0 , N 0, 4

QS and RS are angle bisectors of QPR. Find each measure.

12. the distance from S to PR 13. m SQP

In DEF, DJ 30, and FM 12. Find each length.

14. DM 15. MJ

16. GF 17. GM

Find the orthocenter of a triangle with the given vertices.

18. N 2, 2 , P 4, 2 , Q 0, 2 19. R 2, 1 , S 2, 5 , T 4,

20. The vertices of WXY are W 3, 2 , X 5, 2 , and Y 1, 4 . A is the midpoint of WY ,

and B is the midpoint of XY . Show that AB WX and AB 1 __ 2 WX.

Find each measure.

21. DE 22. FG

23. DG 24. m CHF

25. m FHE 26. m CED

Lesson

5-1

Lesson

5-2

Lesson

5-3

Lesson

5-4

8 9.4 50

21.5 36°63°

5.4 5.4

2 1 _

2 , 1

1 _

2 1, 2

6.4 27°

20 10

18 6

0, 0 2, 3

13 5.2

6.5 47°

133° 47°

y 1 = 1 (x 2)


EPS10

Chapter 5

Write an indirect proof of each statement.

27. An isosceles triangle cannot have an obtuse base angle.

28. A right triangle cannot have three congruent sides.

29. Write the angles in 30. Write the sides in order from smallest order from shortest

to largest. to longest.

Tell whether a triangle can have sides with the given lengths. Explain.

31. 4, 7, 8 32. 7, 9, 18 33. 2x 5, 4x, 3 x 2 , when x 3

The lengths of two sides of a triangle are given. Find the range of possible lengths for the third side.

34. 4 in., 10 in. 35. 8 ft, 8 ft 36. 6.2 cm, 12 cm

Compare the given measures.

37. Compare RS and UV. 38. Compare m XWY 39. Find the range of and m ZWY. values for x.


Given: m X m Y, m B m A

Prove: AY XB

Find the value of x. Give your answer in simplest radical form.

41. 42. 43.

Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

44. 45. 46.

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

47. 4, 7.5, 8.5 48. 6, 10, 11 49. 9, 21, 25

Find the value of x. Give your answer in simplest radical form.

50. 51. 52.

Find the values of x and y. Give your answers in simplest radical form.

53.

54. 55.

Lesson

5-5

Lesson

5-6

Lesson

5-7

Lesson

5-8

K, J, H LN , MN , LM



RS UV

m XWY m ZWY

5 _

6 x

4 _

3

7.5

149 6 5

50; yes

3 13 ; no 24; yes

yes; right yes; acute yes; obtuse

8 2 5 2 3


9 3 ; 18 4 3 ; 8 3 12 3 ; 18

EPS11

Park


1. Building The guy wires −−

AB and −−

CB supporting a cell phone tower are congruent and are equally spaced from the base of the tower. How do these wires ensure that the cell phone tower is perpendicular to the ground? (Lesson 5-1)

2. Safety City planners want to relocate their town’s firehouse so that it is the same distance from the three main streets of the town. Draw a sketch to show where the firehouse should be positioned. Justify your sketch.(Lesson 5-2)

3. Safety A lifeguard needs to watch three areas of a water park. Draw a sketch to show where she should stand to be the same distance from all the swimmers. Justify your sketch.(Lesson 5-2)

4. Art An artist is designing a sculpture composed of a pedestal with a triangular top. The vertices of the top are A (-4, 2) , B (2, 4) , and C (4, -3) . Where should the artist attach the pedestal so that the triangle is balanced? (Lesson 5-3)

5. Measurement City engineers plan to build a bridge across the pond shown. What will be the length of the bridge, GH? (Lesson 5-4)

Engineering Use the following information for Exercises 6 and 7.

Playground engineers are planning a sidewalk that will connect the swings, seesaw, and slide.(Lesson 5-5)

6. If the angle at the swings is the largest, which portion of the sidewalk will be the longest?

7. The distance from the swings to the slide is 37 ft. Can the lengths of the other sides be 40 ft and 50 ft? Explain.

8. Geography The cities of Allenville, Baytown, College City, and Dean Park are shown on the map. Baytown and Dean Park are each 30 miles from College City. Which city is closer to Allenville: Baytown or Dean Park? (Lesson 5-6)

9. Mark is late for school. He usually goes around the park so he can walk along the water. Today he decides to cut through the park. About how many feet does he save by going through the park? (Lesson 5-7)

10. Sports A baseball diamond is a square with a side length of 90 ft. What is the distance from first base to third base? (Lesson 5-8)

11. Recreation Haley, who is 5 ft tall, is flying a kite on 100 ft of string. How high is the kite? (Lesson 5-8)

25 m

Baytown

about 178 ft

5 + 50 √ # 3 ft, or about 91.6 ft







EPA6

Chapter 5

Extra Practice

EPCH5

CC BGE TE Extra Practice 13-2amhs.ccsdschools.com/UserFiles/Servers/Server_2856713/File/Staff... · See Additional Answers. EPS3 Extra Practice Applications Practice Athletics Use

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