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Understanding the Properties of Parallelograms: Key Theorems and Applications

This section covers the essential properties of parallelograms, defining a parallelogram as a quadrilateral with both pairs of opposite sides parallel. Key theorems are introduced, including the congruence of opposite sides and angles, the supplementary nature of consecutive angles, and the fact that diagonals bisect each other. The quadrilateral PQRS is used as an example to illustrate these concepts. Additionally, practice problems can be found on page 313 of the textbook to reinforce understanding of these geometric properties.

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Understanding the Properties of Parallelograms: Key Theorems and Applications

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  1. 6.2 Properties of Parallelograms Textbook pg 310

  2. Definition: A Parallelogram is a quadrilateral where BOTH pairs of opposite sides are parallel • In PQRS, PQ SR and QR PS P Q R S

  3. Theorem: If a quadrilateral is a parallelogram, then its opposite sides are congruent • In PQRS, PQ = SR and QR = PS P Q R S

  4. Theorem: If a quadrilateral is a parallelogram, then its opposite angles are congruent • In PQRS, <P = <R and <Q = <S P Q R S

  5. Theorem: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary • In PQRS, xo + yo = 180o 180o P Q xo yo 180o 180o yo xo R S 180o

  6. Theorem: If a quadrilateral is a parallelogram, then diagonals bisect each other • In PQRS, QM = MS and PM = MR 180o P Q 180o M 180o R S 180o

  7. Practice • Assignment # • Textbook page 313 • Problems 1-12 all, 13-33 odd, 44 – 53 all

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