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Geometry Section 6-2B Geometry Section 6-2B Proving Quadrilaterals Proving Quadrilaterals are Parallelogramsare Parallelograms

Page 423Page 423Be ready to grade 6-2ABe ready to grade 6-2A

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Answers for 6-2A

1. 132. 443. 135o

4. 122o

5. 98o

6. Diagonals bisect7. Opposite sides are congruent8. Consecutive angles are supplementary9. Opposite angles are congruent10. a. ZW YX, ZY WX (2 pts.)

b. ZWYX, ZYWX (2 pts.) c. W&X, X&Y, Y&Z, Z&W (4 pts.) d. ZWXXYZ, WXYYZW (2 pts.)

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Answers for 6-2A cont.

11. (6,5), (2,5), (4,-1) (3 pts.)

12. 10 pts. (Order may be different, ask if you have a question.)1. ABCD is a parallelogram – Given2. Draw AC 2 pts. determine a line3. AB DC def. of parallelogram4. AD BC def of parallelogram5. DAC BCA alt. int. angles are congruent6. ACD BAC alt. int. angles are congruent7. AC AC Reflexive8. ADC CBA ASA9. AB CD CPCTC 10. BC AD CPCTC

32 pts. possible

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GRADE SCALE – 32 POSSIBLE31.5 – 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%

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Parallelograms:Parallelograms:You can be sure that a quadrilateral is a

parallelogram if both pairs of opposite sides are parallel. (definition of parallelogram)

…if both pairs of opposite sides are parallel.A quadrilateral is a parallelogram…

…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.

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Try It:Try It:

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Is this a parallelogram? Justify your answer.

Yes, the opposite sides are congruent.

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Try It:Try It:

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Is this a parallelogram? Justify your answer.

Yes, the diagonals bisect each other.

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Try It:Try It:

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Is this a parallelogram? Justify your answer.

Yes, the consecutive angles are supplementary.

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Try It:Try It:

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Is this a parallelogram? Justify your answer.

Maybe. BOTH sets of opposite sides must be

parallel.

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Exercises:Exercises:

#4

Pg.425

If AE EC and DE EB, is this a

parallelogram? Justify your answer.

Yes, the diagonals bisect each other.

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Exercises:Exercises:

#5

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If ADC ABC, is this a parallelogram? Justify your answer.

Perhaps. Must have 2 sets of congruent opposite

angles.

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Exercises:Exercises:

#6

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If AB CD and AD BC, is this a parallelogram?

Justify your answer.

Yes, the opposite sides are congruent.

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Exercises:Exercises:

#7

Pg.425

If ABCD and AD BC, is this a parallelogram?

Justify your answer.

Yes, the opposite sides are parallel.

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Exercises:Exercises:

#10

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What values for x and y guarantee that the quadrilateral

is a parallelogram. Justify your answer.

Opposite sides are congruent.

5y = 40y = 8

4x = 20x = 5

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Exercises:Exercises:

#11

Pg.426

What values for x and y guarantee that the quadrilateral

is a parallelogram. Justify your answer.

Alternate interior angles are congruent.

8y = 64y = 8

3x + 6 = 273x = 21x = 7

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Exercises:Exercises:

#12

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What values for x and y guarantee that the quadrilateral

is a parallelogram. Justify your answer.

Consecutive angles are supplementary

5x + y + 4x – y = 1809x = 180

5(20) + y = 125100 + y = 125

y = 25x = 20

Opposite angles are congruent

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m n Given

1 2 Given

1 3 Alt. Int. ‘s are .

If corresponding angles formed by a transversal cutting 2 lines are congruent, then the lines are parallel.

#15

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3 2 Transitive property p q

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