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**6.2 Properties of Parallelograms**

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**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

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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

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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

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**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

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**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

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

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**Using properties of parallelograms**

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

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

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**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 °

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Proving Quadrilaterals are Parallelograms. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Proving Quadrilaterals are Parallelograms. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

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