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6.2-6.3: Parallelograms

This resource provides a comprehensive overview of parallelograms, defining them as quadrilaterals with both pairs of opposite sides parallel. It highlights key properties, such as the congruence of alternate interior and corresponding angles, as well as supplementary same-side interior angles. Students will learn how to use these properties to prove that a quadrilateral is a parallelogram. The document includes examples and assignments for practice, making it an essential guide for mastering theorems related to parallelograms in geometry.

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6.2-6.3: Parallelograms

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  1. 6.2-6.3: Parallelograms • Objectives: • Be able to use some properties of parallelograms. • Be able to prove that a quadrilateral is a parallelogram.

  2. Parallelograms A parallelogram is a quadrilateral with both pairs of opposite sides parallel. REMEMBER, If two lines are parallel, then: P S 1) Alternate interior angles are congruent 2) Alternate exterior angles are congruent 3) Corresponding angles are congruent 4) Same-side interior angles are supplementary. Q R When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are parallel. For example, in the diagram above, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

  3. Theorems about Parallelograms S P Q R S P R Q P S R Q S P M R Q

  4. Example 1) Find the value of each variable in the parallelogram below.

  5. Example: W Z Y X

  6. Example: S P P Q Q R

  7. Example:

  8. Theorems about Parallelograms S P Q R S P R Q P S R Q S P R Q

  9. Theorems about Parallelograms S P Q R Summary

  10. Assignment: • Read pages 330-333 and 338-341 • Pages 333-334 #4-36 EVENS • Pages 342-343 #9-19 ALL

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