6.2 Properties of Parallelograms -...
Transcript of 6.2 Properties of Parallelograms -...
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6.2 Properties of Parallelograms
Goal 1: Use some properties of parallelograms
Use properties of parallelograms in real-life situations
CAS 4, 7, 12
Parallelogram
A parallelogram is a quadrilateral with both pairs of opposite sides parallel and congruent.
P
Q R
S
This is parallelogram: PQRS
QR//PS
SR//PQ
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Theorem 6.2
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
PSQR
P
Q R
S
This is parallelogram: PQRS
SRPQ
Theorem 6.3
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
RP
P
Q R
S
This is parallelogram: PQRS
SQ
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Theorem 6.4
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
180SmPm
P
Q R
S
This is parallelogram: PQRS
180RmQm
Theorem 6.5
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
TSQT
P
Q R
S
This is parallelogram: PQRS
T
RTPT
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Regular Polygons
Any polygons that are both equilateral and equiangular are “regular” polygons
Ex. A Square
Ex. 1 GHJK is a parallelogram. Find the unknown length.
a) JH
b) LH
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Ex. 2 In ABCD, mC =105⁰, Find
the missing angle measures.
Ex. 3 WXYZ is a parallelogram. Find the angle measure of x.
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Ex. 4 UVWX is a parallelogram.
1. If XU=15 and UW=28, find WZ.
2. If m∡VWX=120⁰, find m∡WXU
3. If m∡UVW=55⁰ and m∡VWX 7x-8, find x.