1. 8.2 Properties of Parallelograms
Geometry

2. Objectives: Use some properties of parallelograms.
Use properties of parallelograms in real-lie situations

3. In this lesson . . .
And the rest of the chapter, you will study special quadrilaterals. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

4. If a quadrilateral is a parallelogram, then
Both pairs of opposite sides are congruent
Both pairs of opposite angles are congruent
Any pair of consecutive angles are supplementary, and
The diagonals bisect each other

5. Theorems about parallelogramsQ R
—If a quadrilateral is a parallelogram, then its opposite sides are congruent.
►PQ≅RS and SP≅QR P S

6. Theorems about parallelogramsQ R
—If a quadrilateral is a parallelogram, then its opposite angles are congruent.
P ≅ R and
Q ≅ S P S

7. Theorems about parallelogramsQ R
—If a quadrilateral is a parallelogram, then its consecutive angles are supplementary (add up to 180°).
mP +mQ = 180°,
mQ +mR = 180°,
mR + mS = 180°,
mS + mP = 180° P S

8. Theorems about parallelogramsQ R
—If a quadrilateral is a parallelogram, then its diagonals bisect each other.
QM ≅ SM and
PM ≅ RM P S

9. Ex. 1: Using properties of Parallelograms5 F G
FGHJ is a parallelogram. Find the unknown length. Explain your reasoning. JH JK 3 K H J b.

10. Ex. 2: Using properties of parallelogramsQ R
PQRS is a parallelogram.
Find the angle measure.
mR
mQ
70° P S

11. Ex. 3: Using Algebra with ParallelogramsQ
PQRS is a parallelogram. Find the value of x.
mS + mR = 180°
3x = 180
3x = 60
x = 20
3x°
120° S R
Consecutive s of a □ are supplementary.
Substitute 3x for mS and 120 for mR.
Subtract 120 from each side.
Divide each side by 3.

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