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

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

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

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

5. 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

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

7. 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

8. 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

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