1. Geometry 7-4 Area of Trapezoids, Rhombuses, and Kites

2. Review

3. Areas

4. Area Area of a Triangle

5. Theorem The Pythagorean theorem In a right triangle, the sum of the squares of the legs of the triangle equals the square of the hypotenuse of the triangle A C b B a c

6. Theorem Converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. A C b B a c

7. Converse of Pythagorean

8. Theorem 45° – 45° – 90° Triangle In a 45° – 45° – 90° triangle the hypotenuse is the square root of two times as long as each leg

9. Theorem 30° – 60° – 90° Triangle In a 30° – 60° – 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of three times as long as the shorter leg

10. New Material

11. Investigation Get your supplies Paper Scissors Ruler

12. Investigation Construct a trapezoid, and label it as shown Find the height, by folding Cut it out

13. Investigation Make & label a copy

14. Investigation Arrange the two trapezoids to form a figure for which you already know the formula for the area

15. Investigation Arrange the two trapezoids to form a figure for which you already know the formula for the area

16. Conjecture Trapezoid Area Conjecture The area of a trapezoid is given by the formula A = ½ (B 1 + B 2 ) x H, where A is the area, B 1 and B 2 are the lengths of the two bases, and H is the height of the trapezoid

17. Example

20. Sample Problems

21. Investigation Get your supplies Paper Scissors Ruler

22. Investigation Cut out a large kite (folding the paper first will make this easy)

23. Investigation Clearly mark and label each diagonal d1 d2

24. Investigation Cut the kite into pieces, and arrange to make a shape with a known area d1 d2

25. Conjecture Kite Area Conjecture The area of a kite is given by the formula A = ½ d 1 x d 2 where A is the area, and d 1 and d 2 are the diagonals of the kite

26. Investigation Rhombus We previously calculated the area of a parallelogram, is there an easier formula for the area of a rhombus?

27. Theorems

28. Practice

31. Sample Problems

34. Practice

38. Sample Problems

40. Practice

43. Homework Pages 376 – 379 1 – 4, 11, 13 – 20, 22, 29, 34 – 37, 48, 49, 50