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Parallelograms

Parallelograms. Advanced Geometry Polygons Lesson 2. Parallelogram. both pairs of opposite sides are parallel. Characteristics of Parallelograms. Opposite sides are congruent. Opposite angles are congruent. Characteristics of Parallelograms (cont.).

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Parallelograms

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  1. Parallelograms Advanced Geometry Polygons Lesson 2

  2. Parallelogram both pairs of opposite sides are parallel

  3. Characteristics of Parallelograms • Opposite sides are congruent. • Opposite angles are congruent.

  4. Characteristics of Parallelograms (cont.) • Consecutive angles are supplementary.

  5. Characteristics of Parallelograms (cont.) • The diagonals of a parallelogram bisect each other.

  6. Characteristics of Parallelograms (cont.) • Each diagonal separates the parallelogram into two congruent triangles.

  7. Example: Quadrilateral RSTU is a parallelogram. Find RS, y, m∠UTR, m∠STU, and m∠RST.

  8. Example: Parallelogram JKLM has diagonals and that intersect at N. If JN = 6x – 4, JL = 8x, NM = x + 3y, and KN = 2y + 7, find x, y, and KM.

  9. Example: Use the definition of parallelogram to verify that quadrilateral LMNP is a parallelogram.

  10. Characteristics Parallelogram • Def.: opp. sides parallel • opp. sides  • opp. angles  • consec. angles supp. • diagonals bisect each other • each diagonal creates  triangles

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