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Pythagorean Theorem In a right triangle with sides of length a and b and hypotenuse c : a 2 + b 2 = c 2 MA202 Sections 5 & 401 Chapter 12-3 Slides Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides Proving the

SLIDE 1

Pythagorean Theorem

In a right triangle with sides of length a and b and hypotenuse c: a2 + b2 = c2

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 2

Proving the Pythagorean Theorem

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 3

Proving the Pythagorean Theorem

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 4

Example 12.16

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 5

Converse of the Pythagorean Theorem

If you have a triangle with sides of length a, b, and c, where a2 + b2 = c2: then the triangle is a right triangle with hypotenuse the side of length c.

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 6

Example 12.18

Determine if each of the following is a right triangle: 15, 17, 8

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 7

Example 12.18

Determine if each of the following is a right triangle: 15, 17, 8

(Yes, 82 + 152 = 64 + 225 = 289 = 172)

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 8

Example 12.18

Determine if each of the following is a right triangle: 15, 17, 8

(Yes, 82 + 152 = 64 + 225 = 289 = 172)

10, 5, 5 √ 3

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 9

Example 12.18

Determine if each of the following is a right triangle: 15, 17, 8

(Yes, 82 + 152 = 64 + 225 = 289 = 172)

10, 5, 5 √ 3

(Yes, 52 + (5

√ 3)2 = 25 + 75 = 100 = 102)

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 10

Example 12.18

Determine if each of the following is a right triangle: 15, 17, 8

(Yes, 82 + 152 = 64 + 225 = 289 = 172)

10, 5, 5 √ 3

(Yes, 52 + (5

√ 3)2 = 25 + 75 = 100 = 102) 5, 11, 12

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 11

Example 12.18

Determine if each of the following is a right triangle: 15, 17, 8

(Yes, 82 + 152 = 64 + 225 = 289 = 172)

10, 5, 5 √ 3

(Yes, 52 + (5

√ 3)2 = 25 + 75 = 100 = 102) 5, 11, 12

(No, 52 + 112 = 25 + 121 = 146 = 122)

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 12

Class Discussion

In a square based right regular pyramid, the height off the square is measured from the center of the square. For some of the homework, remember the formulas for area from the previous section.

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 13

Class Discussion

Solve for x in the following figure:

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 14

Class Discussion

Solve for y in the following figure:

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 15

Class Discussion

Solve for x and y in the following figure:

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 16

Class Discussion

Find the area of the equilateral triangle:

MA202 Sections 5 & 401 Chapter 12-3 Slides

SLIDE 17

Homework

Homework 7 (due 4/6/10): Section 12.3 # 2ac, 3, 4ab, 5, 6, 9, 32 Section 12.4 # 2b, 3c, 4d, 5d, 6ab, 19a, 23

MA202 Sections 5 & 401 Chapter 12-3 Slides