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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.

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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. QR S P

4 Theorems 6.4 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. m

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

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Using Algebra with Parallelograms PQRS is a parallelogram. Find the value of h. PQ RS 3h120° 3h = h = h = 20

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

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

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Examples Use the diagram of parallelogram JKLM. Complete the statement. K L MJ N LM NK

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Find the measure in parallelogram LMNQ. 1. LM 2. LP 3. LQ 4. QP 5. m

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