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 _____________. congruent opposite

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

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

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

2. Find mB and mC. 119° 61°

3. Find mJ and mK. 102° 78°

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

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

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

HI = _________ 16 Opposite sides 

GH = _________ 8 Diagonals bisect each other

KH = _________ 10 Opposite sides 

HJ = _________ 16 8 Diagonals bisect each other

KIH = _________ 28° Alternate interior angles

180 – 84 = JIH = _________ 96° Consecutive angles are supplementary

KJI = _________ 84° Opposite angles are 

96 – 28 = HKI = _________ 68° 96° Opposite angles are 

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 parallel parallelogram

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

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

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

both pairs of opposite angles 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?

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? 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 8.2 #34 52u Ans: –2x + 37 = x – 5 M 4y + 5 N x = 14 Section Page # Assignment Spiral 8.2 8.3 517 518-520 526-527 Guided Practice #3-6 3-13 odd, 14, 34 2-6, 8, 15, 17, 19, 21 6-8 Ans: –2x + 37 = x – 5 M 4y + 5 N x = 14 –2x + 37 x – 5 4y + 5 = y + 14 y = 3 Q y + 14 P P = 17 + 17 + 9 + 9 = 52u