Tests for Parallelograms Lesson 8-3 Tests for Parallelograms

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

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

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 e) Diagonals Bisect Each Other A B M C D

Determine whether the quadrilateral is a parallelogram 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. Example 3-3a

Determine whether 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. Example 3-3b

Find x so that the quadrilateral is a parallelogram. B C D Opposite sides of a parallelogram are congruent. Substitution Distributive Property Subtract 3x from each side. Add 1 to each side. Answer: When x is 7, ABCD is a parallelogram. Example 3-4a

Find y so that the quadrilateral is a parallelogram. Opposite angles of a parallelogram are congruent. Substitution Subtract 6y from each side. Subtract 28 from each side. Divide each side by –1. Answer: DEFG is a parallelogram when y is 14. Example 3-4c

Find m and n so that each quadrilateral is a parallelogram. b. Answer: Answer: Example 3-4e

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: Homework: 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