Transcript 6.2 Properties of Parallelograms GOAL PROPERTIES OF PARALLELOGRAMS Learn the notation given on page 330! Learn the definition of parallelograms and the theorems listed on.

6.2 Properties of Parallelograms
GOAL
1
PROPERTIES OF PARALLELOGRAMS
Learn the notation given on page 330!
Learn the definition of parallelograms and the theorems
listed on page 330!
EXAMPLE 1
Extra Example 1
GHJK is a parallelogram.
Find the unknown length.
K
8
a. JH
b. LH
Solution
J
6
L
G
H
EXAMPLE 2
Extra Example 2
In ABCD, mC  105. Find the angle measure.
a. mA
b. mD
Solution
EXAMPLE 3
Extra Example 3
WXYZ is a parallelogram.
Find the value of x.
W
(3x + 18)°
Z
(4x - 9)°
X
Solution
Y
Checkpoint
U
UVWX is a parallelogram.
1. If XU  15 and UW  28, find WZ.
14
V
Z
X
2. If mVWX  120, find mWXU.
60°
3. If mUVW  55 and mVWX  7 x  8, find x.
x = 19
W
6.2 Properties of Parallelograms
GOAL
2
REASONING ABOUT PARALLELOGRAMS
EXAMPLE 4
EXAMPLE 5
Extra Example 4
Given: ABCD is a parallelogram.
Prove: 2  4
A
B
2
1
4
D
3
C
Extra Example 5
B
A
C
Given: ACDF is a parallelogram.
ABDE is a parallelogram.
Prove: BCD  EFA
F
E
D
Checkpoint
E
You can use linear pairs to show
that mEAD  mDAB  mFCB
mDCB. What postulate or
theorem can you then use with the
substitution and subtraction
properties of equality and the
definition of congruence to show
that EAD  FCB ?
Opp. s
A
B
D
C
F
.
EXAMPLE 6
Extra Example 6
A four-sided concrete slab has consecutive angle measures
of 85°, 94°, 85°, and 96°. Is the slab a parallelogram?
Explain.
No; if it were, then by Theorem 6.3 both pairs of opp.
angles would be congruent, not just one pair.
Checkpoint
Each circle in the crystal
lattice shown represents a
molecule. ABED and BCFE
are parallelograms. A, B, and
C are collinear, as are D, E,
and F. Must ACFD be a
parallelogram? Explain.
A
D
B
E
C
F
Yes. Since segments AB and DE are parallel and
contained in segments AC and DF, then segments AC
and DF must be parallel. Also, since segments AD
and CF are both parallel to segment BE, they are
parallel to each other.
QUESTION:
What are 5 properties of parallelograms?
ANSWER:
1. Opposite sides are parallel.
2. Opposite sides are congruent.
3. Opposite angles are congruent.
4. Consecutive angles are supplementary.
5. Diagonals bisect each other.
BONUS POINT:
6. The sum of the interior angles is 360°.