Geometry - Loudoun County Public Schools / Overvie€¦ · Web viewThe student will solve real-world problems involving angles of polygons. Syllabus: Ch 8 Quadrilaterals. Block

SOL G.9

SOL G.10

Name: _____________________ Block:_________ Date: ____________________

Notes: Chapter 8

Quadrilaterals

Sections Covered: 1.6 Classify Polygons8.1 Find Angle Measures in Polygons 8.2 Properties of Parallelograms8.3 Proving ParallelogramsTessellationsTransformations8.4 Properties of Rhombuses, Rectangles, & Squares 8.5 Properties of Trapezoids and Kites

The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems.

The student will solve real-world problems involving angles of polygons.

2

Syllabus: Ch 8 Quadrilaterals

Block

Date In Class At Home

11Discover the Angle Formulas Activity

Notes 1.6 Classify Polygons and 8.1 Find Angle Measures in Polygons

1.6 and 8.1 Practice ProblemsG.2 SOL Review

12 Notes 8.2 Properties of Parallelograms and 8.3 Proving Parallelograms

8.2 and 8.3 Practice ProblemsG.5 SOL Review

13 Review 8.1-8.3Tessellations Review 8.1-8.3

14 Quiz 8.1-8.3Transformations

Transformations Practice Problems

15Notes 8.4 Properties of Rhombuses,

Rectangles, and Squares, Notes 8.5 Use Properties of Trapezoids

8.4 and 8.5 Practice ProblemsSOL G.6

16 Review Ch 8 Review Ch 8

17 Ch 8 Test Review G.7

***Syllabus subject to change due to weather, pep rallies, illness, etc

Need Help?Your teacher ie available for extra help. Email them to set up a time!Mu Alpha Theta is Monday, Thursday, and Friday mornings in L409.

Need to make up a test/quiz?Math Make Up Room is open Tues/Thurs/Fri mornings and Mon/Wed/ Thurs afternoons.

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Notes: 1.6 Classify Polygons

_____________________________________________

Definition of Polygon: A polygon is a closed figure formed by a finite number of coplanar segments such that:

1.) the sides that have a common endpoint are non-collinear2.) each side intersects exactly two other sides, but only at their endpoints

Convex Polygon Concave Polygon (Non-convex)a polygon such that no line containing a polygon such a line containing a side a side of the polygon contains a point on of the polygon has a point on the the interior of the polygon interior of the polygon

Example: Example:

Polygons are classified by the ____________ _____ ___________.

Classifying Polygons by Sides: Number of

SidesClassification (Name)

34567891012n

4

Ex1: Determine if the figure is a polygon. If so, classify it as convex or non-convex.

1. 2. 3.

4. 5. 6.

Regular Polygon: A convex polygon with all sides and angles congruent.

Draw an example of a regular polygon Draw an example of an irregular polygon

Notes: 8.1 Find Angle Measures in Polygons

Interior Angles of a Polygon: Exterior Angles of a Polygon: Sum of the interior angles of a convex polygon: Sum of the exterior angles of a convex polygon,

one angle at each vertex:

Measure of each interior angle of a regular n-gon: Measure of each exterior angle of a regular n-gon:

5

Ex1: Find the value x. (Objects are not drawn to scale.)

1. 2.

What relationship do you notice about an exterior angle and its interior angle? **This is a very important hint**

Ex2: Find the sum of the measures of the interior angles of each convex polygon.

1. 11-gon 2. 16-gon 3. 30-gon

Ex3: The measure of one exterior angle of a regular polygon is given below. Find the number of sides of the polygon.

1. 30° 2. 20° 3. 5°

Ex4: The sum of the measures of the interior angles of a convex polygon is given below. Determine the number of sides of the polygon.

1. 2160° 2. 6120° 3. 4140°

6

x + 15

2x

x + 15

2x 5x - 15

3x - 14x + 38

5x + 15

TIP: WHENEVER POSSIBLE, WORK WITH THE EXTERIOR. THE SUM IS ALWAYS THE

SAME.

Ex5: The measure of an interior angle of a regular polygon is 157.5°. Find the number of sides of the polygon.

Ex6: Find the sum of the measures of the exterior angles of a convex polygon with 8 sides.

Ex7: Find the measure of ∠1. (Objects not drawn to scale.)

1. 2.

3. 4.

7

∠1

110°90°

150° 140°135°

106°

114°

153°

102°

126°

103°

144°

∠1

∠1

∠1

Notes 8.2: Properties of Parallelograms

_____________________________________________

Parallelogram

Notation:Properties of Parallelograms:If a quadrilateral is a parallelogram, then…

1.

2.

3.

4.

5.

Think “COOOD”ies

Ex1: ABCD is a parallelogram. Given mABD = 65, mCBD = 45, AE = 5, BC = 8. Find the measure of the following:

AD = _____EC = _____mADC = _____mBCD = _____mBDA = _____

Ex2:

8

A

B C

D

E

7y+1

6y+10

2x+103x

Ex3: Find x and y for each parallelogram.

1. 2.

3. 4.

Ex4:

9

yx

72

3x-9

2x+312y+214y+5

3y-15 4x

2x

Notes 8.3: Proving Parallelograms

_____________________________________________

If _________________________________________ of a quadrilateral are ___________________, then the quadrilateral is a __________________.

Determine if the following quadrilateral is a parallelogram. Justify your answer.

New Theorems:




10


If_________________________________________ of a quadrilateral are ___________________, and ___________________, then the quadrilateral is a __________________.




All Mixed Up: Determine if the following quadrilaterals are parallelograms. If so, state the theorem you used.

11

7. Prove that quadrilateral ABCD is a parallelogram.

SUMMARIZE5 Properties of a parallelogram: 5 ways to prove that a quadrilateral is a parallelogram:1. 1.2. 2.3. 3.4. 4.5. 5.

Notes: Tessellations

_____________________________________________

Tessellation-

12

5.

6.

Regular Tessellation-

The sum of the measures surrounding a point (or vertex) must be ______________

Can these figures form a regular tessellation?

A 20 sided figure? A 10 sided figure? A 12 sided figure?

Note: No regular polygon with more than _______ sides can be used in a regular tessellation.

13

14

Semi-regular tessellation:Irregular Tessellation:

Summary:1. At each vertex of a tessellation, the sum of the measures of the angles must

equal 360.2. Any quadrilateral will tessellate.3. Combinations of figures can be used to tessellate.4. Only equilateral triangles, squares, and regular hexagons can make regular

tessellations.

Practice:

15

Notes 8.4: Properties of Rhombuses, Rectangles, and Squares

____________________________________________

Rhombus _______________________________

Special Properties: 1.

2.

Rectangle _______________________________

Special Properties: 1.

Square _______________________________

Special Properties 1.

2.

3.

REMEMBER:Properties of Parallelograms:

16

Use Rectangle ABCD to solve each problem.

1.

2.

3.

4.

17

E

CD

A B

E

CD

A B

E

CD

A B

E

CD

A B

Use Rhombus ABCD to solve each problem.

5. mBCE = _______ 6. mBEC = _______

7. AC = _______ 8. mABD = _______

9. AD = _______

Use Square ABCD to solve each problem.

10. mAEB = 3x. Find x.

11. mBAC = 9x. Find x.

12.

18

14

12

59EB

D

C

A

E

B

C

A

D

E

B

C

A

D

E

B

C

A

D

Notes 8.5: Properties of Trapezoids

____________________________________________

Trapezoid - has _____________________ pair of sides

-legs are ________________________________

Isosceles Trapezoid - has _____________________ pair of sides

legs are _____________ base angles are __________ diagonals are __________

Midsegment Theorem for Trapezoids- midsegment is to _______________________

- midsegment = ½ (__________ + ____________)

Practice: Solve for x.

Practice Coordinate Geometry: Determine if quadrilateral PQRS is a parallelogram, rhombus, rectangle, square, or trapezoid. List all that apply.

19

12in

x

x + 5

20in

3x - 1

4x - 3

1.

2.

3.

20

Geometry - Loudoun County Public Schools / Overvie€¦ · Web viewThe student will solve real-world problems involving angles of polygons. Syllabus: Ch 8 Quadrilaterals. Block

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