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Lesson 8-3

Lesson 8-3. Tests for Parallelograms. Transparency 8-3. 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

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Lesson 8-3

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  1. Lesson 8-3 Tests for Parallelograms

  2. Transparency 8-3 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? A B D C 5-Minute Check on Lesson 8-2 6(x+5) S R (12y+19)° (8y+1)° T U 12x+6 Standardized Test Practice: X W WX  YZ A WZ  XZ B Y Z X  Z W  Y C D Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 8-3 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? A B BC DC D C 5-Minute Check on Lesson 8-2 Opposite sides are congruent Opposite sides are congruent D Opposite angles are congruent 6(x+5) S R (12y+19)° (8y+1)° T U 4 8 12x+6 Standardized Test Practice: X W WX  YZ A WZ  XZ B Y Z X  Z W  Y C D Click the mouse button or press the Space Bar to display the answers.

  4. 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

  5. Vocabulary • None new

  6. 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

  7. Example 3-3a 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.

  8. Example 3-3b 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.

  9. A B D C Example 3-4a Find x so that the quadrilateral is a parallelogram. 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.

  10. D E G F Example 3-4c 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.

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

  12. 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

  13. 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

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