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Geometry Section 6-2B Proving Quadrilaterals are Parallelograms Page 423 Be ready to grade 6-2A

Geometry Section 6-2B Proving Quadrilaterals are Parallelograms Page 423 Be ready to grade 6-2A. Answers for 6-2A. 13 44 135 o 122 o 98 o Diagonals bisect Opposite sides are congruent Consecutive angles are supplementary Opposite angles are congruent

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Geometry Section 6-2B Proving Quadrilaterals are Parallelograms Page 423 Be ready to grade 6-2A

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  1. Geometry Section 6-2B Proving Quadrilaterals are ParallelogramsPage 423Be ready to grade 6-2A

  2. Answers for 6-2A • 13 • 44 • 135o • 122o • 98o • Diagonals bisect • Opposite sides are congruent • Consecutive angles are supplementary • Opposite angles are congruent • a. ZW YX, ZY WX (2 pts.)b. ZW@YX, ZY@WX (2 pts.) c. W&X, X&Y, Y&Z, Z&W (4 pts.) d. ÐZWX@ÐXYZ, ÐWXY@ÐYZW (2 pts.)

  3. Answers for 6-2A cont. • 11. (6,5), (2,5), (4,-1) (3 pts.) • 10 pts. (Order may be different, ask if you have a question.) • ABCD is a parallelogram – Given • Draw AC 2 pts. determine a line • AB DC def. of parallelogram • AD BC def of parallelogram • ÐDAC @ÐBCA alt. int. angles are congruent • ÐACD @ÐBAC alt. int. angles are congruent • AC @ AC Reflexive • DADC @DCBA ASA • AB @ CD CPCTC • BC @ AD CPCTC 32 pts. possible

  4. GRADE SCALE – 32 POSSIBLE 31.5 – 98% 24.5 – 77% 31 – 97% 24 – 75% 30.5 – 95% 23.5 – 73% 30 – 94% 23 – 72% 29.5 – 92% 22.5 – 70% 29 – 91% 22 – 69% 28.5 – 89% 21.5 – 67% 28 – 88% 21 – 66% 27.5 – 86% 20.5 – 64% 27 – 84% 20 – 63% 26.5 – 83% 19.5 – 61% 26 – 81% 19 – 59% 25.5 – 80% 18.5 – 58% 25 – 78% 18 – 56% 4

  5. Parallelograms: You can be sure that a quadrilateral is a parallelogram if both pairs of opposite sides are parallel. (definition of parallelogram) A quadrilateral is a parallelogram… …if both pairs of opposite sides are parallel. Pg.425 …if both pairs of opposite angles are congruent. …if both pairs of opposite sides are congruent. …if consecutive angles are supplementary. …if the diagonals bisect each other.

  6. Try It: Is this a parallelogram? Justify your answer. Yes, the opposite sides are congruent. Pg.424

  7. Try It: Is this a parallelogram? Justify your answer. Yes, the diagonals bisect each other. Pg.424

  8. Try It: Is this a parallelogram? Justify your answer. Yes, the consecutive angles are supplementary. Pg.424

  9. Try It: Is this a parallelogram? Justify your answer. Maybe. BOTH sets of opposite sides must be parallel. Pg.424

  10. Exercises: If AE @ EC and DE @ EB, is this a parallelogram? Justify your answer. #4 Pg.425 Yes, the diagonals bisect each other.

  11. Exercises: If ÐADC @ÐABC, is this a parallelogram? Justify your answer. #5 Pg.425 Perhaps. Must have 2 sets of congruent opposite angles.

  12. Exercises: If AB @ CD and AD @ BC, is this a parallelogram? Justify your answer. #6 Pg.425 Yes, the opposite sides are congruent.

  13. Exercises: If ABCD and AD BC, is this a parallelogram? Justify your answer. #7 Pg.425 Yes, the opposite sides are parallel.

  14. Exercises: What values for x and y guarantee that the quadrilateral is a parallelogram. Justify your answer. #10 Pg.426 Opposite sides are congruent. 4x = 20 5y = 40 y = 8 x = 5

  15. Exercises: What values for x and y guarantee that the quadrilateral is a parallelogram. Justify your answer. #11 Pg.426 Alternate interior angles are congruent. 3x + 6 = 27 8y = 64 y = 8 3x = 21 x = 7

  16. Exercises: What values for x and y guarantee that the quadrilateral is a parallelogram. Justify your answer. #12 Pg.426 Opposite angles are congruent Consecutive angles are supplementary 5(20) + y = 125 5x + y + 4x – y = 180 9x = 180 100 + y = 125 x = 20 y = 25

  17. #15 Pg.426 m n Given Ð1 @Ð2 Given Ð1 @Ð3 Alt. Int. Бs are @. Ð3 @Ð2 Transitive property p q If corresponding angles formed by a transversal cutting 2 lines are congruent, then the lines are parallel.

  18. Homework: Practice 6-2B (Be sure to justify even if you say “no”.)

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