1. Bellwork  Solve for x A E D B C GH EF 2x+10 5x-32 x 2 -2xx2x2 Clickers

2. Bellwork Solution  Solve for x A E D B C 2x+10 5x-32

3. Bellwork Solution  Solve for x GH EF x 2 -2xx2x2

4. Section 8.4

5. The Concept  Today we’re going to extend our understanding of quadrilaterals to include three special kinds of quadrilaterals  We’ve seen these three before, but not formally

6. Corollaries Rhombus Corollary A quadrilateral is a rhombus if and only if it has four congruent sides Rectangle Corollary A quadrilateral is a rectangle if and only if it has four right angles Square Corollary A quadrilateral is a square if and only if it is a rhombus and a rectangle Why are these corollaries and not their own theorems?

7. Intersections Vertex Axis of symmetry Rhombuses Square Rectangle

8. Theorems Theorem 8.11: A parallelogram is a rhombus if and only if its diagonals are perpendicular Theorem 8.12: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles

9. Theorems Theorem 8.13: A parallelogram is a rectangle if and only if its diagonals are congruent

10. On your own What kind of quadrilateral is described below? Vertex Axis of symmetry Not Equilateral Diagonals bisect each other into 4 congruent pieces

11. On your own What kind of quadrilateral is described below? Vertex Axis of symmetry Opposite angles are congruent

12. On your own What kind of quadrilateral is described below? Vertex Axis of symmetry Equilateral & Equiangular

13. On your own What kind of quadrilateral is described below? Vertex Axis of symmetry Equilateral, diagonals are perpendicular

14. Homework  8.4 1, 2-16 even, 17, 19-29, 33-48 mult 3

15. On your own Answer to #8

16. On your own Answer to #17 Vertex Axis of symmetry

17. On your own Answer to #24 Vertex Axis of symmetry

18. On your own What polygon do we see? Vertex Axis of symmetry

19. On your own What polygon do we see? Vertex Axis of symmetry

20. Most Important Points  Rhombuses  Rectangles  Squares