1. 6.2 Properties of Parallelograms

2. Properties of Parallelograms
Theorem 6.2
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
PQ = RS and SP = QR
Theorem 6.3
If a quadrilateral is a parallelogram, then it opposite angles are congruent.
<P = < R and < Q = < S
Theorem 6.4
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
m<P + m<Q = 180o, m<Q + m<R = 180o
m<R + m<S = 180o, m<S + m<P = 180o
Theorem 6.5
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
QM = SM and PM = RM _ ~
Q R
P S

3. Theorems
6.2 If a quadrilateral is a parallelogram, then its opposite sides are congruent.
6.3 If a quadrilateral is a parallelogram, then its opposite angles are congruent. Q R S P

4. Theorems
6.4 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
m<P + m<Q = 180°
m<Q + m<R = 180°
m<R + m<S = 180°
m<S + m<P = 180° Q R S P

5. Using Properties of Parallelograms
PQRS is a parallelogram. Find the angle measure.
m< R
m< Q Q R
70 ° + m < Q = 180 °
m< Q = 110 °
70° P S

6. Using Algebra with Parallelograms
PQRS is a parallelogram. Find the value of h.
3h = 1800
3h = 60 P Q
h = 20 3h
120° S R

7. Theorems
6.5 If a quadrilateral is a parallelogram, then its diagonals bisect each other. R Q M P S

8. Using properties of parallelograms
FGHJ is a parallelogram. Find the unknown length. JH JK 5 3 F 5 G 3 K J H

9. Examples
Use the diagram of parallelogram JKLM. Complete the statement. LM K L NK
<KJM N
<LMJ NL MJ J M

10. Find the measure in parallelogram LMNQ.18 LM LP LQ QP
m<LMN
m<NQL
m<MNQ
m<LMQ 8 L M 9
110° 10 10
70° 9 P 8
70 °
32°
110 ° Q N 18
32 °