6.2 Properties of Parallelograms

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# 6.2 Properties of Parallelograms - PowerPoint PPT Presentation

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.

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Presentation Transcript
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.