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Understanding Parallelograms: Properties, Theorems, and Proofs

Dive into the study of parallelograms with comprehensive explanations of key concepts such as definitions, properties, and theorems. Discover the Parallelogram Theorem, its properties (congruent opposite sides and angles, supplementary consecutive angles), and how the diagonals bisect each other. Learn to identify and prove parallelograms through conditions such as congruent opposite sides and angles. This guide provides an essential foundation for understanding the unique characteristics of parallelograms in geometry.

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Understanding Parallelograms: Properties, Theorems, and Proofs

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  1. 8-1 Angles of Polygons Vocab: diagonal

  2. Theorem 8.1

  3. Example 1

  4. Theorem 8.2

  5. Example 2

  6. 8-2 Parallelograms Vocab: parallelogram

  7. Parallelogram • A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

  8. Properties of parallelograms • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • If it has one right angle, it has four right angles

  9. Diagonals of Parallelograms • The diagonals of a parallelogram bisect eachother. • RQ = QT • UQ = QS

  10. Diagonal separates congruent triangles • Each diagonal separates the parallelogram into two congruent triangles.

  11. 8.3 Tests for Parallelograms

  12. Proving Parallelograms • If both pairs of opposite sides are congruent, • If both pairs of opposite angles are congruent, • If the diagonals bisect each other, • If one pair of opposite sides is both parallel and congruent, • then the quadrilateral is a parallelogram.

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