Lesson 8-3

Tests for Parallelograms

Complete each statement about parallelogram ABCD

1. AB ______

2. AD ______

3. D ______

In the figure RSTU is a parallelogramFind the indicated value.

4. x 5. y

6. Which congruence statement is not necessarily true, if WXYZ is a parallelogram?

5-Minute Check on Lesson 8-25-Minute Check on Lesson 8-25-Minute Check on Lesson 8-25-Minute Check on Lesson 8-2 Transparency 8-3

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Standardized Test Practice:

A

C

B

D

WZ XZ

A B

CD

R S

TU

6(x+5)

(12y+19)°

(8y+1)°

12x+6

W X

YZ

WX YZ

W Y X Z

Complete each statement about parallelogram ABCD

1. AB ______

2. AD ______

3. D ______

In the figure RSTU is a parallelogramFind the indicated value.

4. x 5. y

6. Which congruence statement is not necessarily true, if WXYZ is a parallelogram?

5-Minute Check on Lesson 8-25-Minute Check on Lesson 8-25-Minute Check on Lesson 8-25-Minute Check on Lesson 8-2 Transparency 8-3

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Standardized Test Practice:

A

C

B

D

WZ XZ

A B

CD

R S

TU

6(x+5)

(12y+19)°

(8y+1)°

12x+6

W X

YZ

WX YZ

W Y X Z

Opposite sides are congruent

Opposite sides are congruent

Opposite angles are congruent

DC

BC

D

4 8

Objectives

• Recognize the conditions that ensure a quadrilateral is a parallelogram– A quadrilateral is a parallelogram if any of the

following is true:• Both pairs of opposite sides are parallel • Both pairs of opposite sides are congruent• Both pairs of opposite angles are congruent• Diagonals bisect each other• A pair of opposite sides is both parallel and congruent

• Prove that a set of points forms a parallelogram in the coordinate plane

Vocabulary

• None new

Tests for Parallelograms

A B

C D

M

Quadrilateral is a Parallelogram (if any of the following are true):

a) Both Pairs of Opposite Sides Are Parallel

b) Both Pairs of Opposite Sides Are Congruent

c) A Pair of Opposite Sides Is Both Parallel and Congruent

d) Both Pairs of Opposite Angles Are Congruent

e) Diagonals Bisect Each Other

Determine whether the quadrilateral is a parallelogram. Justify your answer.

Answer: Each pair of opposite sides have the same measure. Therefore, they are congruent. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

Determine whether the quadrilateral is a parallelogram. Justify your answer.

Answer: One pair of opposite sides is parallel and has the same measure, which means these sides are congruent. If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

Find x so that the quadrilateral is a parallelogram.

Opposite sides of a parallelogram are congruent.

A B

CD

Substitution

Distributive Property

Add 1 to each side.

Answer: When x is 7, ABCD is a parallelogram.

Subtract 3x from each side.

Find y so that the quadrilateral is a parallelogram.

Opposite angles of a parallelogram are congruent.

F

D E

G

Subtract 6y from each side.

Substitution

Subtract 28 from each side.

Divide each side by –1.

Answer: DEFG is a parallelogram when y is 14.

Find m and n so that each quadrilateral is a parallelogram.

Answer: Answer:

a. b.

Ch 8 Quiz 1 Need to Know

• Angles in Convex Polygons (n = # of sides) – Interior angle + Exterior angle = 180°– Sum of Interior angles = (n-2) 180°– Sum of Exterior angles = 360°– Shortcut for sides (360° / exterior angle) = n

• Parallelogram Characteristics– Opposite sides parallel and congruent ()– Opposite angles congruent ()– Consecutive angles supplementary (add to 180°)– Diagonals bisect each other

Summary & Homework

• Summary:– A quadrilateral is a parallelogram if any of

the following is true:• Both pairs of opposite sides are parallel and

congruent• Both pairs of opposite angles are congruent• Diagonals bisect each other• A pair of opposite sides is both parallel and

congruent

• Homework: – pg 421-423; 15-22, 26-27, 45-46