1. WARM UP Pass out progress reports! Get a Calendar from the front!

2. RIGHT TRIANGLES AND THE PYTHAGOREAN THEOREM

3. ON GRAPH PAPER… Draw a rectangle Label the dimensions a and b Cut out 4 rectangles that are a x b Label the sides a and b -inside the rectangle Cut each rectangle on one diagonal Label your new sides as c Cut out 3 squares: one with sides a, one with sides b, and one with sides c

4. WHAT NOW… Make 2 groups 4 triangles and the 2 smaller squares Four triangles and the big square Make a big square from each group, no overlapping parts (you will have 2 squares)

5. QUESTIONS: What is each side length? What is the area of each square? What can you say about the relationship of the 3 squares? Use a ruler, measure sides a, b and c. Plug these values into your expression, does it work?

6. HYPOTENUSE Longest Side Across from the RIGHT ANGLE Only in right triangles

7. THE PYTHAGOREAN THEOREM If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2

8. SOLVE FOR THE VARIABLE-IN SIMPLEST RADICAL FORM y = 60 y = 5√5 2√772 √ 19

9. A rhombus has diagonals of 12 cm and 20 cm. What is the perimeter of the rhombus? in simplest radical form

10. A window washer has an 18-ft ladder. He needs to reach the bottom of a window 16 feet of the ground. How far out from the building should the base of the ladder be? Round to the nearest tenth of a foot.

11. CONVERSE OF THE PYTHAGOREAN THEOREM If the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse, then the triangle is a right triangle. a 2 + b 2 = c 2

12. IS IT A RIGHT TRIANGLE? YesYes No

13. A 2 + B 2 < C 2 THINK IN TERMS OF C OBTUSE If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is OBTUSE.

14. A 2 + B 2 > C 2THINK IN TERMS OF C ACUTE If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is ACUTE.

15. CLASSIFY THE TRIANGLE 9, 11, 16 10, 12, 14 24, 70, 74 Obtuse Acute Right

16. CAN ANY 3 LENGTHS MAKE A TRIANGLE? 1, 2, 3 2, 3, 4 3, 4, 8 Cut your paper into pieces that have a length of 1, 2, 3, 4, & 8 cm. Try to create the triangle given.

17. TRIANGLE SIDES To make a triangle, the two smaller sides must have a SUM that is GREATER than the third side.

18. IS THIS A TRIANGLE?? 2, 4, 5 6, 7, 14 3, 6, 9 YES NO

19. AREA OF A TRIANGLE Half the product of a base and the corresponding height A = ½ bh

20. FIND THE AREA 56ft 2 13.75ft 2

21. FINDING AREA USING TRIANGLE TRIG Given SAS, the area of the triangle is half the product of the lengths of two sides and the sine of the included angle. A = ½ bc(SinA) A = ½ ac(SinB) A = ½ ab(SinC )

22. TRY SOME 11.1 m 2 35.9 in 2 86 in 2

23. HOMEWORK Worksheet