Unit 6 Lesson 2 Properties of Parallelograms Parallelogram

Unit 6 Lesson 2 - Properties of Parallelograms

Parallelogram: Quadrilateral with both pairs of opposite sides parallel

Theorem: If a quadrilateral is a parallelogram, then both pairs of ______ opposite sides are _______. congruent

Theorem: If a quadrilateral is a parallelogram, then both congruent pairs of ______ opposite angles are _______.

Theorem: If a quadrilateral is a parallelogram, then both pairs of ______ consecutive angles are _______. supplementary A B m A + m B = 180° m A + m D = 180° D C m B + m C = 180° m C + m D = 180°

Theorem: If a quadrilateral is a parallelogram, then both diagonals ________ each other. bisect

1. Find the value of each variable in the parallelogram. 8 11

1. Find the value of each variable in the parallelogram. a – 3 = 14 a = 17 b+2=7 b=5

1. Find the value of each variable in the parallelogram. g + 7 = 15 g=8 h – 8 = 12 h = 20

1. Find the value of each variable in the parallelogram. 3 x + 6 = 12 3 x = 6 x=2 2 y + 9 = 27 2 y = 18 y=9

2. Find m B and m C. 119° 61°

3. Find m J and m K. 102° 78°

4. Find the value of each variable in the parallelogram. x+2 3 x 3 x = 6 x=2 6 y– 1 x+2=y– 1 2+2=y– 1 4=y– 1 5=y

4. Find the value of each variable in the parallelogram. 9 b – 2 = 106 9 b = 108 b = 12° 7 a – 3 + 106 = 180 7 a + 103 = 180 7 a = 77 a = 11°

4. Find the value of each variable in the parallelogram. 5 q + 4 = 49 5 q = 45 q=9 2 p = 124 p = 62°

16 HI = _____ Opposite sides

8 GH = _____ Diagonals bisect each other

10 KH = _____ Opposite sides

16 HJ = _____ 8 Diagonals bisect each other

28° KIH = _____ Alternate interior angles

180 – 84 = 96° JIH = _____ Consecutive angles are supplementary

84° KJI = _____ Opposite angles are

96 – 28 = 68° HKI = _____ 96° Opposite angles are

If opposite sides of a quadrilateral are congruent ________, then the quadrilateral is a parallelogram ________.

If both pairs of opposite angles are congruent _________, then the quadrilateral is parallelogram a _________.

supplementary If consecutive angles are ________, parallelogram then the quadrilateral is a ________.

bisect If the diagonals ______ each other, parallelogram then the quadrilateral is a ________.

If one pair of opposite sides are ______ congruent parallel and ______, then the quadrilateral is a parallelogram ________.

What theorem can you use to show the quadrilateral is a parallelogram? one pair of opposite sides are congruent and parallel

What theorem can you use to show the quadrilateral is a parallelogram? the diagonals bisect each other

What theorem can you use to show the quadrilateral is a parallelogram? both pairs of opposite sides are congruent

What theorem can you use to show the quadrilateral is a parallelogram? both pairs of opposite angles are congruent

Is the quadrilateral a parallelogram? Explain. No, Both pairs of opposite sides are not parallel

Is the quadrilateral a parallelogram? Explain. Yes, Both pairs of opposite sides are congruent

Is the quadrilateral a parallelogram? Explain. No, Not a quadrilateral!

Is the quadrilateral a parallelogram? Explain. No, Opposite sides are not congruent

What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram?

What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram?

What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram?

What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram? m CDA + m DAB = 180° m CDA + m DCB = 180°

What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram? DCB DAB CDA CBA

HW Problem LTs 6. 2, 6. 3 Page # Assignment 517 Guided Practice #3 -6 (FRONT PAGE) 518 -520 3 -13 odd, 14, 34 (FRONT PAGE) 526 -527 2 -6, 8, 15, 17, 19, 21 (BACK PAGE) Due