6 2 Properties of Parallelograms Learning Target I

6. 2 Properties of Parallelograms Learning Target: I can use properties of parallelograms.

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

Theorems Ý 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 P R S

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

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

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

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

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

Find the measure in parallelogram LMNQ. 1. 2. 3. 4. 5. 6. 7. 8. LM 18 LP 8 LQ 9 QP 10 m<LMN 70° m<NQL 70 ° m<MNQ 110 ° m<LMQ 32 ° L 110° M 10 P Q 32° 18 9 8 N

Pair-share on 6. 2 Practice A ã Work on page 334 #20 -37 ã