1. Section 6-4/6-5 (1B): Special Parallelograms, Trapezoids and Kites March 16, 2012

2. Warm-up: (15 mins)  Practice Book (6-2), p. 66: #2 – 8 (even), 9 -12, 14 – 20 (even)  Practice Book (6-3), p. 68: # 1 – 6 (even), 13 - 20

3. Warm-up

5.  Practice Book (6-2), p. 66: #2 – 8 (even), 9 -12, 14 – 20 (even)  Practice Book (6-3), p. 68: # 1 – 6, 13 - 20

6. Warm-up

7. Questions on Homework?

8. Sections 6-4 and 6-5: Special Parallelograms, Trapezoids and Kites  Objectives: You will learn to use properties of diagonals of rhombuses and rectangles, and properties of trapezoids and kites.

9. Properties of Quadrilaterals Parallelogram  Opposite sides are parallel  Opposite sides are congruent  Opposite angles are congruent  Consecutive angles are supplementary  Diagonals bisect each other Rhombus: Parallelogram with 4 congruent sides  Properties of Parallelogram  All sides are congruent  Each diagonal bisects opposite angles  Diagonals are perpendicular

10. Properties of Quadrilaterals Rectangle: Parallelogram with 4 right angles  Properties of Parallelogram  All angles are right angles  Diagonals are congruent Square: Parallelogram with 4 congruent sides (rhombus) and 4 right angles (rectangle)  Properties of Parallelogram  Properties of Rhombus  Properties of Rectangle

11. Properties of Quadrilaterals

12. Example 1 Find measures of the numbered angles for this rhombus

13. Example 2 Find measures of the numbered angles for these rhombuses

14. Example 3 Find missing angles and value of x in rectangle JOSH

15. Example 4 Find missing angles and value of y in rectangle CODY

16. Copy and Fill in Table PropertyParallelogramRhombusRectangleSquare All sides are ≅ Opposite sides are ≅ Opposite sides are || Opposite angles are ≅ All angles are right ∠ ’s Diagonals bisect each other Diagonals are ≅ Diagonals are ┴ Each diagonal bisects opposite angles

17. Section 6-5: Trapezoids and Kites Trapezoid  Parallel sides are called bases.  Non-parallel sides are called legs.  Angles that share a leg are supplementary.

18. Section 6-5: Trapezoids and Kites Isosceles Trapezoid  Properties of a trapezoid  Legs are congruent (def)  Base angles are congruent (Thm 6-15)  Diagonals are congruent (Thm 6-16)

19. Section 6-5: Trapezoids and Kites Kite  Diagonals are perpendicular  A diagonal bisects the angles formed by the congruent sides  Angles formed by non-congruent sides are congruent

20. Kite Applet http://www.mathopenref.com/kite.html

21. Example 1: Find requested angle measures

22. Example 2: Find value of x in isosceles trapezoid SEAN

23. Example 3: Find perimeter of isosceles trapezoid CARL

24. Example 4: Find missing angle measures in KITE

25. Example 5: Find x and y

26. Example 6: Find x

27. Summary: Fill in everything you know Isosceles Trapezoid Kite

28. Wrap-up  Today you learned to use properties of diagonals of rhombuses and rectangles and about trapezoids and kites.  Monday you’ll learn about figures on the coordinate plane. !!!! Reminder: Quiz on Monday !!!! Homework  p. 315 – 317, # 1-21 (odd), 48-50, 57  p. 322 – 324, # 1-15 (odd), 18, 21-29 (odd)