10.4 Two Special Right Triangles

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10.4 Two Special Right Triangles

• Chapter 10 Pythagorean Theorem

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Review

• Simplifying square roots

?50
?25?2
?25??2
5??2
?84
?4?21
?4??21
2??21
?126
?9?14
?9??14
3??14

• Multiplying square roots

(?3??2)
(?6)
(?5)2
(?5)
?(?5)
5
(2?3)2
(2?3)
4?3
?(2?3)
12
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Isosceles Right Triangle

• Angle measure 45-45-90
• A right triangle with 2 sides congruent

x
x
x
c
x
x
c
c
x
Turn to page 489
X2 X2 c2
2X2 c2
?2X2 ?c2
X?2 c
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Isosceles Right Triangle Conjecture

• In an isosceles right triangle (45-45-90), if the
  legs have length x, then the hypotenuse has
  length x?2

x?2
x
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Examples

• Solve for x

18
x
10
18?2
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30-60-90 Right Triangle

• Angle measure 30-60-90
• It is half of an equilateral triangle

What are mlta and mltb?
They are both 60 degrees
What are mltacd and mltbcd?
They are both 30 degrees
What are mltadc and mltbdc?
They are both 90 degrees
How do you think ac compares to ad?
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30-60 Right Triangle

• C-91 conjecture
  In a 30-60-90 triangle, if the side
  opposite the 30? angle has length x, then the
  hypotenuse has length 2x.

• C-92 conjecture
  In a 30-60-90 triangle, if the shorter
  leg has length x, then the longer leg has length
  x?3

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Examples

• Find a

• Find c

c
60?
The hypotenuse is twice the shorter leg
8?3
If the shorter leg has x, then the longer leg has
x?3
2a 34
C 8?3?3
a 17
C 8(3)
C 24
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Two Special Right Triangles
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Homework

• Page 492
• 1-27, 31, 32
• Worksheet 8-12