Lesson 8 3 Tests for Parallelograms Transparency 8

Lesson 8 -3 Tests for Parallelograms

Transparency 8 -3 5 -Minute Check on Lesson 8 -2 Complete each statement about parallelogram ABCD A B 1. AB ______ 2. AD ______ D C 3. D ______ In the figure RSTU is a parallelogram Find the indicated value. 4. x 6. 5. y 6(x+5) S (12 y+19)° R (8 y+1)° T 12 x+6 U Standardized Test Practice: Which congruence statement is not necessarily true, if WXYZ is a parallelogram? A WX YZ B WZ XZ C W Y D X Z Click the mouse button or press the Space Bar to display the answers. X W Z Y

Transparency 8 -3 5 -Minute Check on Lesson 8 -2 Complete each statement about parallelogram ABCD DC 1. AB ______ Opposite sides are congruent BC 2. AD ______ Opposite sides are congruent D 3. D ______ Opposite angles are congruent In the figure RSTU is a parallelogram Find the indicated value. 4. x 6. 5. 4 y B D C 6(x+5) S (12 y+19)° R 8 A (8 y+1)° T 12 x+6 U Standardized Test Practice: Which congruence statement is not necessarily true, if WXYZ is a parallelogram? A WX YZ B WZ XZ C W Y D X Z Click the mouse button or press the Space Bar to display the answers. X W Z Y

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 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 A B e) Diagonals Bisect Each Other M C D

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. A B D Opposite sides of a parallelogram are congruent. C Substitution Distributive Property Subtract 3 x from each side. Add 1 to each side. Answer: When x is 7, ABCD is a parallelogram.

Find y so that the quadrilateral is a parallelogram. D E Opposite angles of a parallelogram are congruent. G F Substitution Subtract 6 y from each side. 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. a. Answer: b. Answer:

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