8.2 & 8.3 - Properties of Parallelograms

Parallelogram: Quadrilateral with both pairs of opposite sides parallel

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

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

Theorem:If a quadrilateral is a parallelogram, then both pairs of ___________ angles are _____________.consecutive supplementary

A B

CD

mA + mB = 180°

mA + mD = 180°

mB + mC = 180°

mC + mD = 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 = 14a = 17

b + 2 = 7b = 5

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

g + 7 = 15g = 8

h – 8 = 12h = 20

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

3x + 6 = 12

2y + 9 = 272y = 18

3x = 6x = 2

y = 9

2. Find mB and mC.

61°119°

3. Find mJ and mK.

102°

78°

4. Find the value of each variable in the parallelogram.

3x = 6x + 2

y – 1

3x6

x + 2 = y – 1

x = 2

2 + 2 = y – 1 4 = y – 1 5 = y

4. Find the value of each variable in the parallelogram.

9b – 2 = 106

7a – 3 + 106 = 180

9b = 108b = 12°

7a + 103 = 1807a = 77

a = 11°

4. Find the value of each variable in the parallelogram.

5q + 4 = 49

2p = 124p = 62°

5q = 45q = 9

HI = _________16

Opposite sides

GH = _________8

Diagonals bisect each other

KH = _________10

Opposite sides

HJ = _________16

Diagonals bisect each other8

KIH = _________28°

Alternate interior angles

JIH = _________96°

Consecutive angles aresupplementary

180 – 84 =

KJI = _________84°

Opposite angles are

HKI = _________68°

Opposite angles are

96 – 28 =

96°

If opposite sides of a quadrilateral are

________________, then the quadrilateral is a

________________.

congruent

parallelogram

If both pairs of opposite angles are

_________________, then the quadrilateral is

a _________________.

congruent

parallelogram

If consecutive angles are ________________,

then the quadrilateral is a ________________.

supplementary

parallelogram

If the diagonals ____________ each other,

then the quadrilateral is a ________________.

bisect

parallelogram

If one pair of opposite sides are ____________

and ____________, then the quadrilateral is a

________________.

congruent

parallelogram

parallel

What theorem can you use to show the quadrilateral is a parallelogram?

one pair of opposite sides are congruentand 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?

DCAB

BCAD

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

EBDE

ECAE

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

DCAB

CBAD

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

mCDA + mDAB = 180°

mCDA + mDCB = 180°

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

DCB DAB

CDA CBA

Ans:M N

PQ

–2x + 37

y + 14

x – 5

4y + 5 –2x + 37 = x – 5

x = 14

4y + 5 = y + 14

y = 3

17 + 17 + 9 + 9 =P =

8.2 #34

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HW ProblemSecti

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8.2

8.3

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Guided Practice #3-63-13 odd, 14, 342-6, 8, 15, 17, 19, 21

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