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6.2 Properties of ParallelogramsPowerPoint Presentation

6.2 Properties of Parallelograms

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6.2 Properties of Parallelograms

- A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
- In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

Theorem 6.3

- If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Consecutive Angles

- Angles of a polygon that share a side are consecutive angles.

Theorem 6.4

- If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Using Consecutive Angles

- What is the measure of angle P in parallelogram PQRS?
- 26°
- 64°
- 116°
- 126°

Theorem 6.5

- If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Theorem 6.6

- If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Using Algebra to Find Lengths

- Solve a system of linear equations to find the values of x and y in parallelogram KLMN. What are KM and LN?

Theorem 6.7

- If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Using Parallel Lines and Transversals

- In the figure, AE || BF || CG || DH, AB = BC = CD = 2, and EF = 2.25. What is EH?
EF = FG = GH

EH = EF + FG + GH

EH = 2.25 + 2.25 + 2.25

EH = 6.75

More Practice!!!!!

- Homework – p. 364 - 365 #9 – 12, 14 – 27, 29 – 30 ALL.

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