1. 6.2 Properties of Parallelograms

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

3. Theorems
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

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

5. Using Algebra with Parallelograms
PQRS is a parallelogram. Find the value of h. P Q 3h
120° S R

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

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

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

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