G4.2 Properties of Parallelograms Objectives: Use some properties of parallelograms. Use properties of parallelograms in real-life situations. •

Concept: Parallelogram A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Ex:

Concept: Opposite Sides Property The opposite sides of a parallelogram are congruent. PQ≅RS and SP≅QR Q R P S

Concept: Opposite Angles Property The opposite angles of a parallelogram are congruent. Q R LP ≅ LR and LQ ≅ LS P S

Concept: Concsecutive Angles Property The consecutive angles of a parallelogram are supplementary, (add up to 180º) Q R mLP +mLQ = 180°, mLQ +mLR = 180°, mLR + mLS = 180°, mLS + mLP = 180° P S

Concept: Diagonals Property If a quadrilateral is a parallelogram, then its diagonals bisect each other. QM ≅ SM and PM ≅ RM Q R P S

Concept: Using the Properties Find the JH and JK SOLUTION: JH = FG Opposite sides of a are ≅. JH = 5 Since FG = JH then JH = 5

Concept: Using the Properties cont… Find the JH and JK SOLUTION: JK = GK Diagonals of a bisect each other GK = 3 Since JK = GK then JK = 3

Concept: Using the Properties cont… Problem #2 PQRS is parallelogram. Find the measures of the given angles: mLR mLQ 70º 110º