Chapter 10.1: Pythagorean Theorem

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Chapter 10.1 Pythagorean Theorem

• Geometry CP
• Chapter 10 Pythagorean Theorem

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Definitions

• Right triangle - must contain one angle 90

hypotenuse
side opposite the right angle
leg
leg
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Pythagorean Theorem

• a2 b2 c2

Where c hypotenuse a and b are the length of
the legs
c
a
b
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History

• It is unknown when in history we discovered the
  unique relationship between the lengths of the
  sides of a right triangle
• Ancient Babylonians and Chinese recognized the
  relationship. It is believed ancient Egyptians
  did too.
• Pythagoras (572-497 B.C) was a Greek philosopher
  who demonstrated this to be true.

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Example

• How would you use the relationship?

Find the distance between two points
How high up on the wall will a 5 foot latter
reach if the foot of the latter is placed 3 feet
from the wall?
a2 b2 c2
a
Distance of the latter from the wall
Height of wall where latter reaches
b
c
Height of latter
wall
5ft
4ft
32 b2 52
9 b2 25
9-9 b2 25-9
3ft
b2 16
b ?16 4
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Does this work with other triangles?

• What are other triangles?

Acute triangle
Obtuse triangle
25
17
7
6
38
8
62 72 85 gt 82
172 252 914 lt 382
NO!
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Examples

• Find the length of c

a2 b2 c2
29.22 72 c2
c
852.64 49 c2
29.2m
901.64 c2
v901.64 c
30m ? c
7m
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Examples

• Find the length of the rectangle whose width is
  15ft and diagonal is 21ft.

a2 b2 c2
152 b2 212
225 b2 441
21ft
225 b2 -225 441 - 225
b2 216
b ?216
b ? 14.7 ft
15ft
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Homework

• Page 479
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