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6.3

6.3. Showing Quadrilaterals are Parallelograms . We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms . What 5 facts are ALWAYS true about parallelograms? Both pairs of opposite sides are parallel. Both pairs of opposite sides are congruent.

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6.3

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  1. 6.3 Showing Quadrilaterals are Parallelograms

  2. We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms • What 5 facts are ALWAYS true about parallelograms? • Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • One angle is supplementary to both of its consecutive angles. • Diagonals bisect each other.

  3. Example 1 Tell whether the quadrilateral is a parallelogram. Explain your reasoning.

  4. You Try It… • Tell whether each quadrilateral is a parallelogram. Explain your reasoning.

  5. Example 2 • Use the slopes of the segments in the diagram to determine if the quadrilateral is a parallelogram.

  6. You Try It…

  7. Application

  8. 6.4 • Rhombuses • Rectangles • Squares

  9. Vocabulary

  10. Example 1 • A) In the diagram, PQRS is a rhombus. Find QR, RS, and SP. • B) Use the information in the diagram to name the special quadrilateral.

  11. Corollaries Rhombus Corollary: If a quadrilateral has 4 congruent sides, then it is a rhombus. Rectangle Corollary: If a quadrilateral has 4 right angles, then it is a rectangle. Square Corollary: If a quadrilateral has 4 congruent sides and four right angles, then it is a square.

  12. You Try It… • Use the information in the diagram to name the special quadrilateral

  13. Theorems about Diagonals • The diagonals of a rhombus are perpendicular. • The diagonals of rectangle are congruent.

  14. Example 2

  15. You Try It…

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