1. 1 The Pythagorean Theorem

2. 2 A B C Given any right triangle, A 2 + B 2 = C 2

3. 3 Example A B C In the following figure if A = 3 and B = 4, Find C. A 2 + B 2 = C 2 3 2 + 4 2 = C 2 9 + 16 = C 2 5 = C

4. 4 Practice 1) A = 8, B = 15, Find C 2) A = 7, B = 24, Find C 3) A = 9, B= 40, Find C 4) A = 10, B = 24, Find C 5)A = 6, B = 8, Find C 6) A = 9, B = 12, Find C 1) A = 8, B = 15, Find C 2) A = 7, B = 24, Find C 3) A = 9, B= 40, Find C 4) A = 10, B = 24, Find C 5)A = 6, B = 8, Find C 6) A = 9, B = 12, Find C A B C C = 17 C = 25 C = 41 C = 26 C = 10 C = 15

5. 5 Example A B C In the following figure if B = 5 and C = 13, Find A. A 2 + B 2 = C 2 A 2 +5 2 = 13 2 A 2 + 25 = 169 A 2 = 144 A = 12

6. 6 Practice 1)A=8, C =10, Find B 2)A=15, C=17, Find B 3)B =10, C=26, Find A 4)A =12, C=16, Find B 5) B =5, C=10, Find A 6) A=11, C=21, Find B 1)A=8, C =10, Find B 2)A=15, C=17, Find B 3)B =10, C=26, Find A 4)A =12, C=16, Find B 5) B =5, C=10, Find A 6) A=11, C=21, Find B A B C B = 6 B = 8 A = 24 B = 10.6 A = 8.7 B = 17.9

7. “Real-World” 7 The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? Step 1: Draw a sketch and label the parts. Step 2: Determine whether you are looking for the leg or hypotenuse of the right triangle. Step 3: Solve the missing length.

8. AREA 8 Find the area of each figure 1.2.

9. 9 Given the lengths of three sides, how do you know if you have a right triangle? A B C Given A = 6, B=8, and C=10, describe the triangle. A 2 + B 2 = C 2 6 2 +8 2 = 10 2 36 + 64 = 100 100 = 100 This is true, so you have a right triangle. This is true, so you have a right triangle.

10. 10 If C 2 < A 2 + B 2, then you have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. C 2 = A 2 + B 2 6 2 = 4 2 + 5 2 36 = 16 + 25 36 < 41 36 < 41, so we have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. C 2 = A 2 + B 2 6 2 = 4 2 + 5 2 36 = 16 + 25 36 < 41 36 < 41, so we have an acute triangle. A B C

11. 11 If C 2 > A 2 + B 2, then you have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. C 2 = A 2 + B 2 8 2 = 4 2 + 6 2 64 = 16 + 36 64 > 52 64 > 52, so we have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. C 2 = A 2 + B 2 8 2 = 4 2 + 6 2 64 = 16 + 36 64 > 52 64 > 52, so we have an obtuse triangle. A C B

12. 12 Describe the following triangles as acute, right, or obtuse 1)A=10, B=15, C=20 2) A=2, B=5, C=6 3) A=12, B=16, C=20 4) A=11, B=12, C=14 5) A=2, B=3, C=4 6) A=1, B=7, C=7 1)A=10, B=15, C=20 2) A=2, B=5, C=6 3) A=12, B=16, C=20 4) A=11, B=12, C=14 5) A=2, B=3, C=4 6) A=1, B=7, C=7 A B C obtuse acute obtuse right obtuse acute