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The Quadrilateral Family TreeParallelograms
I can use the properties of a parallelogram to solve problems.
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Quadrilateral
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1. Four-sided polygon
Parallelograms
Parallelogram•A quadrilateral with two pairs of parallel
sides
1.
1. Four-sided polygon
QUADRILATERAL
1.
2.
3.
4.
PARALLELOGRAM
2.
3.
1. 1.
2.
3.
1.
2.
3.
1.
2.
ISOSCELES TRAPEZOID
Parallelogram – How can we construct a parallelogram?
Parallelogram
Parallelogram
1
2
Parallelogram
1
2
Parallelogram
1
23
4
Parallelogram
1
23
4
Parallelogram
1
23
4
Parallelogram
1
23
4
Parallelogram
1
23
4
•The two triangles formed by a diagonal are congruent by ASA.
Parallelogram
1
23
4
•What does that mean about opposite sides of a parallelogram?
Parallelogram
1
23
4
•What does that mean about opposite sides of a parallelogram?
CPCTC
1.
TRAPEZOID
1. Four-sided polygonQUADRILATERAL
1.
2.
3.
4.
PARALLELOGRAM
2.
1.
SQUARE
2.
3.
1.
RECTANGLE1.
2.
3.
4.
RHOMBUS
1.
2.
3.
KITE
1.
2.
3.
ISOSCELES TRAPEZOID
1.
1. Four-sided polygon
QUADRILATERAL
2.
3.
4.
PARALLELOGRAM
2.
3.
1. 1.
2. 3.
1.
2.
1. Opposite sides are congruent 2.
3.
1.
Parallelograms•What about opposite angles in a
parallelogram?
1.
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3.
4.
PARALLELOGRAM
2.
3.
1. 1.
2. 3.
1.
2.
1. Opposite sides are congruent 2.
3.
1.
Parallelograms
1
2
•Are these two triangles congruent? By which postulate?
Parallelogram•Since the triangles are congruent, the
diagonals of the parallelogram bisect each other.
1.
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3. Diagonals bisect each other
4.
PARALLELOGRAM
2.
3.
1. 1.
2. 3.
1.
2.
1. Opposite sides are congruent 2.
3.
1.
Parallelogram
5
6
•What kind of angles are angles 5 & 6?
•Consecutive angles in a parallelogram are supplementary.
Parallelogram
5
6
1.
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
PARALLELOGRAM
2.
3.
1. 1.
2. 3.
1.
2.
1. Opposite sides are congruent 2.
3.
1.
ExampleIn CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°.
Find CF.
Find mEFC.
Find DF.
CF = 74 mm
opp. sides
mEFC + mFCD = 180°
mEFC = 138°
cons. s supp.
DF = 2DGDF = 62
diags. bisect each other.
In KLMN, LM = 28 in., LN = 26 in., and mLKN = 74°.
Find KN.
Find mNML.
Find LO.
LM = 28 in.
opp. sides
Your Turn
NML LKN
mNML = 74° opp. s
LN = 2LO
LO = 13 in.
diags. bisect each other.
WXYZ is a parallelogram.
Find YZ.
YZ = 52
Example
WXYZ is a parallelogram.
Find mZ .
Example
mZ = 65°
EFGH is a parallelogram.
Find JG.
JG = 12
Example
EFGH is a parallelogram.
Find FH.
FH = 18
Your Turn
QRST is a parallelogram. Find each measure.
3. TQ
*4. mT
Lesson QuizIn PNWL, NW = 12, PM = 9, and mWLP = 144°.
1. PW
2. mPNW
18
144°
28
71°
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