6.2 Properties of Parallelograms

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Presentation transcript:

6.2 Properties of Parallelograms

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

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

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

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

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

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

Examples 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. 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 °