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.

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6.2 Properties of Parallelograms

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6 2 properties of parallelograms

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

Theorem 6.3

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


Consecutive angles

Consecutive Angles

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


Theorem 6 4

Theorem 6.4

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


Using consecutive angles

Using Consecutive Angles

  • What is the measure of angle P in parallelogram PQRS?

  • 26°

  • 64°

  • 116°

  • 126°


Theorem 6 5

Theorem 6.5

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


Theorem 6 6

Theorem 6.6

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


Using algebra to find lengths

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?


Using algebra to find lengths1

Using Algebra to Find Lengths


Theorem 6 7

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

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

More Practice!!!!!

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


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