6-2 properties of parallelograms. area area of parallelogram a = base x height
TRANSCRIPT
6-2 Properties of Parallelograms
Area
Area of Parallelogram A = base x height
height
base
Proof1.
2.
3.
4.
5.
6.
7.
8.
CB
A D
Given: ABCD is a parallelogramProve: AB DC BC DA <A <C
Proof1.
2.
3.
4.
5.
6.
7.
E
CB
A D
Given: ABCD is a parallelogramProve: EA EC EB ED
TheoremsOpposite sides of a parallelogram are congruent.
Opposite angles of a parallelogram are congruent.
Consecutive angles of a parallelogram are supplementary.
Diagonals of a parallelogram bisect each other.
TheoremsIf three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
AD BE CF and AB BC then DE EF
D
E
FC
B
A
Examples1) Find area of the
parallelogram2) Find area of a parallelogram
with vertices (-5,-3), (-2,3), (2,3) & (-1,-3).
15
12
10
A
D
B
C
Examples3) If AB=3x + 11, BC = 2x
+ 19 and CD = 7x – 17,
find x.
4) If m<BAD = y and
m<ADC = 4y – 70, find y.
5) If m<ABC=2x + 100 and
m<ADC=6x + 84, find
m<BCD.
P
A
D
B
C
Examples
6) If m<BCD=80 and
m<CAD=34, find
m<ACD.
7) If AP=3x, BP=y, CP=6x
- 42, and DP=27 - 2y,
find x &y.
P
A
D
B
C
Examples8) Find EH.
2.52
2
2
H
P
O
E
J
L
K
M
Example: Honors Geometry
Statements Reasons1.2.3.4.5.6.
Given: ABCD is parallelogram BE DF
Prove: AF CE
E
F
A
B C
D