6.3

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.

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

7. You Try It…

8. Application

11. 6.4 • Rhombuses • Rectangles • Squares

12. Vocabulary

13. 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.

14. 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.

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

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

17. Example 2

18. You Try It…