Pythagorean Theorem and its converse

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Pythagorean Theorem and its converse

• Lesson 11.4 Notes

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Pythagorean Theorem

• The Pythagorean Theorem is one of the most famous
  and useful theorems found in plane mathematics.

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Pythagoras

• Greek mathematician Pythagoras was credited with
  the discovery and wrote the 1st proof of the
  theorem in 500 B.C.

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Pythagorean Theorem

• The square of the length of the hypotenuse the
  sum of the squares of the lengths of the 2 legs.

Hypotenuse
Leg
Leg
5
Pythagorean Theorem
a2 b2 c2
c
a
b
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Example 1.
a

• Solve for a if b 5 and c 13

5
13
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Example 1.

• a2 b2 c2
• a2 52 132
• a2 25 169
• a2 144
• a 12

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Example 2.

• Find the
• value of c if
• b 15 and
• a 8.

15
c
8
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Example 2.

• a2 b2 c2
• 82 152 c2
• 64 225 c2
• 289 c2
• 17 c

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Example 3. Find a.
3?2
a
6
11

• Example 3 Solution
• a2 b2 c2
• a2 (3?2)2 62
• a2 92 36
• a2 18 36
• a2 18
• a 3?2

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Example 5.
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Example 5 solution

• a2 b2 c2
• 152 92 c2
• 225 81 c2
• 306 c2
• 3v34 c

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Example 6.

• Find the length of a diagonal of a square with
  sides of length 2?2

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Example 6. Diagram
2?2
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Example 6. Solution

• a2 b2 c2
• (2?2) 2 (2?2) 2 c2
• 42 42 c2
• 8 8 c2
• 16 c2
• 4 c

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Converse of the Pythagorean Thrm.

• If a trianlge has side lengths a, b, and c such
  that , then the triangle is a right
  triangle.
• Ex. Tell whether the triangle is a rt. Triangle
• a. 8, 15, 17 b. 5, 8, 9

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Determining if a Triangle is Right

• a3, b8, and c
• a8, b9, and c11

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HOMEWORK

• Page740 s 4-28 even, 33, 38