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Understanding Parallelograms: Properties, Theorems, and Examples

This section covers the fundamental properties of parallelograms, including key theorems that define their characteristics. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Important theorems discussed include congruence of opposite sides and angles, the supplementary nature of consecutive angles, and the bisection of diagonals. The document presents several examples to illustrate these theorems and their applications, providing essential homework problems to reinforce learning.

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Understanding Parallelograms: Properties, Theorems, and Examples

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  1. Section 8 – 2 Use Properties of Parallelograms

  2. Vocabulary Parallelogram: A quadrilateral with BOTHpairs of opposite sides parallel.

  3. Theorem 8.3 If a quadrilateral is a parallelogram, then its opposite SIDES are congruent. If PQRS is a parallelogram, then and

  4. Theorem 8.4 If a quadrilateral is a parallelogram, then its opposite ANGLES are congruent. If PQRS is a parallelogram, then and

  5. Theorem 8.5 If a quadrilateral is a parallelogram, then its consecutive angles are SUPPLEMENTARY. If PQRS is a parallelogram, then

  6. Theorem 8.6 If a quadrilateral is a parallelogram, then its diagonals bisect each other. If PQRS is a parallelogram, then

  7. Example #1 Find the value of each variable. Theorem 8.4 ∠s are ≅ d – 21 = 105◦ +21 __+21 d = 126◦ Theorem 8.3 sides are ≅ z – 8 = 20 +8 __+8 z = 28

  8. Example #2 Find the measure of . Theorem 8.5 are supplementary 51◦ + = 180◦ -51 _______-51 = 129◦

  9. Example #3 Find the value of each variable in the parallelogram. Theorem 8.6 diagonals bisect each other. b – 1 = 9 a = 3

  10. Homework Section 8-2 Page 518 – 521 3 – 11, 13 – 15, 18 – 28 even, 29, 49 - 52

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