10.5

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10.5 The Pythagorean Theorem
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• leg
• leg

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• hypotenuse
• leg
• leg

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• hypotenuse
• leg
• leg
• Pythagorean Theorem For a right triangle with
  legs a and b and hypotenuse c, then a2
  b2 c2, where a is the smaller of the two
  legs.

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

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• Ex. 1 Find the length of the missing side.
• a 25
• 10
• a2 b2 c2

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• Ex. 1 Find the length of the missing side.
• a 25
• 10
• a2 b2 c2
• a2 (10)2 (25)2

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• Ex. 1 Find the length of the missing side.
• a 25
• 10
• a2 b2 c2
• a2 (10)2 (25)2
• a2 100 625

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• Ex. 1 Find the length of the missing side.
• a 25
• 10
• a2 b2 c2
• a2 (10)2 (25)2
• a2 100 625
• a2 525

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• Ex. 1 Find the length of the missing side.
• a 25
• 10
• a2 b2 c2
• a2 (10)2 (25)2
• a2 100 625
• a2 525
• a 22.91

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

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

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• Ex. 2 Determine whether the following side
  measures form right triangles.
• a. 20, 21, 29
• Shorter lengths must be the legs.
• So, a2 b2 c2

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• Ex. 2 Determine whether the following side
  measures form right triangles.
• a. 20, 21, 29
• Shorter lengths must be the legs.
• So, a2 b2 c2
• (20)2 (21)2 (29)2

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• Ex. 2 Determine whether the following side
  measures form right triangles.
• a. 20, 21, 29
• Shorter lengths must be the legs.
• So, a2 b2 c2
• (20)2 (21)2 (29)2
• 400 441 841

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• Ex. 2 Determine whether the following side
  measures form right triangles.
• a. 20, 21, 29
• Shorter lengths must be the legs.
• So, a2 b2 c2
• (20)2 (21)2 (29)2
• 400 441 841
• 841 841

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• Ex. 2 Determine whether the following side
  measures form right triangles.
• a. 20, 21, 29
• Shorter lengths must be the legs.
• So, a2 b2 c2
• (20)2 (21)2 (29)2
• 400 441 841
• 841 841
• , so they form a rt. triangle!