Name: ______Block:______Date: ______

Notes:

Chapter 8

Quadrilaterals

Sections Covered:

1.6 Classify Polygons

8.1 Find Angle Measures in Polygons

8.2 Properties of Parallelograms

8.3 Proving Parallelograms

Tessellations

Transformations

8.4 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.

Syllabus: Ch 8 Quadrilaterals

Block / Date / In Class / At Home
11 / Discover the Angle Formulas Activity
Notes 1.6 Classify Polygons and 8.1 Find Angle Measures in Polygons / 1.6 and 8.1 Practice Problems
G.2 SOL Review
12 / Notes 8.2 Properties of Parallelograms and 8.3 Proving Parallelograms / 8.2 and 8.3 Practice Problems
G.5 SOL Review
13 / Review 8.1-8.3
Tessellations / Review 8.1-8.3
14 / Quiz 8.1-8.3
Transformations / Transformations Practice Problems
15 / Notes 8.4 Properties of Rhombuses, Rectangles, and Squares, Notes 8.5 Use Properties of Trapezoids / 8.4 and 8.5 Practice Problems
SOL 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

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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-collinear

2.) each side intersects exactly two other sides, but only at their endpoints

Convex Polygon Concave Polygon (Non-convex)

a polygon such that no line containinga 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 polygoninterior of the polygon

Example:Example:

Polygons are classified by the ______.

Classifying Polygons by Sides:

Number of Sides / Classification (Name)
3 /
4 /
5
6
7
8
9 /
10
12
n

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 aregular n-gon:

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-gon2. 16-gon3. 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°


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.

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 mABD = 65, mCBD = 45, AE = 5, BC = 8. Find the measure of the following:

AD = _____

EC = _____

mADC = _____

mBCD = _____

mBDA = _____

Ex2:

Ex3: Find x and y for each parallelogram.

1. 2.

3. 4.

Ex4:

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:

If ______of a quadrilateral are ______, then the quadrilateral is a ______.

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

If ______of a quadrilateral are ______, then the quadrilateral is a ______.

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

If______of a quadrilateral are ______, and ______, then the quadrilateral is a ______.

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

If ______of a quadrilateral are ______, then the quadrilateral is a ______.

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

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

7. Prove that quadrilateral ABCD is a parallelogram.

SUMMARIZE

5 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-

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.


1

Semi-regular tessellation:

Irregular Tessellation:

1

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:

Notes 8.4: Properties of Rhombuses, Rectangles, and Squares

______

Rhombus  ______

Special Properties: 1.

2.

Rectangle  ______

Special Properties: 1.

Square  ______

Special Properties1.

2.

3.

REMEMBER:

Properties of Parallelograms:

Use Rectangle ABCD to solve each problem.

1.

2.

3.

4.

Use Rhombus ABCD to solve each problem.

5. mBCE = ______6. mBEC = ______

7. AC = ______8. mABD = ______

9. AD = ______

Use Square ABCD to solve each problem.

10. mAEB = 3x. Find x.

11. mBAC = 9x. Find x.

12.

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.

1.

2.

3.

1