Chapter 8.3
Proving Parallelograms
Geometry
Objective:
1. Recognize the conditions that make a quadrilateral a parallelogram
2. Prove that a set of points forms a parallelogram in the coordinate plane
A.
There are five tests for parallelograms.
(ways to prove that a quadrilateral is a parallelogram)
1.
(Definition) If both pairs of opposite sides of a quadrilateral are ___________, then the quadrilateral is a parallelogram.
If (or )
2.
If both pairs of opposite _______of a quadrilateral are __________, then the quadrilateral is a parallelogram.
If 3.
If both pairs of opposite _______of a quadrilateral are __________, then the quadrilateral is a parallelogram.
If 4.
If the __________ of a quadrilateral __________ each other, then the quadrilateral is a parallelogram.
If
5.
If ____ _____ of opposite sides is both _________ and _________, then the quadrilateral is a parallelogram.
If B.
Examples Determine whether each quadrilateral is a parallelogram.
If so, state the theorem.
7
4
4
7
.
4
4
Chapter 8.3
C.
Proofs
1. Given:
Cont'd
ΔPTS ≅ ΔRTQ
P
Q
T
Prove:
PQRS is a R
S
1.
Given
2.
2.
CPCTC
3.
3.
Def'n segment bisector
1.
4.
ΔPTS ≅ ΔRTQ
PQRS is a
2. Given:
Prove:
1.
3.
.
A
<1 ≅ <2; AB ≅ DC
ABCD is a <1 ≅ <2; AB ≅ DC
1
D
1.
2
Given
2.
2.
3.
4.
ABCD is a
3.
Use the definition to determine whether ABCD is a parallelogram. A(­3, 3), B(2, 5), C(5, 2), D(0, 0)
B
C