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10.5 – The Pythagorean Theorem. leg legleg hypotenuse hypotenuse leg legleg.

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Presentation on theme: "10.5 – The Pythagorean Theorem. leg legleg hypotenuse hypotenuse leg legleg."— Presentation transcript:

1 10.5 – The Pythagorean Theorem

2

3 leg legleg

4 hypotenuse hypotenuse leg legleg

5 hypotenuse hypotenuse leg legleg Pythagorean Theorem: For a right triangle with legs a and b and hypotenuse c, then a 2 + b 2 = c 2, where a is the smaller of the two legs.

6 Ex. 1 Find the length of the missing side. a 25 a 25 10 10

7 Ex. 1 Find the length of the missing side. a 25 a 25 10 10 a 2 + b 2 = c 2 a 2 + b 2 = c 2

8 Ex. 1 Find the length of the missing side. a 25 a 25 10 10 a 2 + b 2 = c 2 a 2 + b 2 = c 2 a 2 + (10) 2 = (25) 2 a 2 + (10) 2 = (25) 2

9 Ex. 1 Find the length of the missing side. a 25 a 25 10 10 a 2 + b 2 = c 2 a 2 + b 2 = c 2 a 2 + (10) 2 = (25) 2 a 2 + (10) 2 = (25) 2 a 2 + 100 = 625 a 2 + 100 = 625

10 Ex. 1 Find the length of the missing side. a 25 a 25 10 10 a 2 + b 2 = c 2 a 2 + b 2 = c 2 a 2 + (10) 2 = (25) 2 a 2 + (10) 2 = (25) 2 a 2 + 100 = 625 a 2 + 100 = 625 a 2 = 525 a 2 = 525

11 Ex. 1 Find the length of the missing side. a 25 a 25 10 10 a 2 + b 2 = c 2 a 2 + b 2 = c 2 a 2 + (10) 2 = (25) 2 a 2 + (10) 2 = (25) 2 a 2 + 100 = 625 a 2 + 100 = 625 a 2 = 525 a 2 = 525 a ≈ 22.91 a ≈ 22.91

12 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29

13 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs.

14 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a 2 + b 2 = c 2

15 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a 2 + b 2 = c 2 (20) 2 + (21) 2 = (29) 2 (20) 2 + (21) 2 = (29) 2

16 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a 2 + b 2 = c 2 (20) 2 + (21) 2 = (29) 2 (20) 2 + (21) 2 = (29) 2 400 + 441 = 841 400 + 441 = 841

17 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a 2 + b 2 = c 2 (20) 2 + (21) 2 = (29) 2 (20) 2 + (21) 2 = (29) 2 400 + 441 = 841 400 + 441 = 841 841 = 841 841 = 841

18 Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a 2 + b 2 = c 2 (20) 2 + (21) 2 = (29) 2 (20) 2 + (21) 2 = (29) 2 400 + 441 = 841 400 + 441 = 841 841 = 841 841 = 841, so they form a rt. triangle!, so they form a rt. triangle!


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