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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: - PowerPoint PPT Presentation
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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
52u
HW ProblemSecti
onPage # Assignment Spira
l
8.2
8.3
517518-520526-527
Guided Practice #3-63-13 odd, 14, 342-6, 8, 15, 17, 19, 21
6-8