Lesson 7.3 Two Special Right Triangles

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Lesson 7.3 Two Special Right Triangles

• Objectives
• To use properties of 45-45-90 triangles
• To use properties of 30-60-90 triangles

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Isosceles Right Triangle Theorem
ISOSCELES RIGHT TRIANGLE THEOREM In an
isosceles right triangle, if the legs have
length, l, then the hypotenuse has length ____.

NOTE If you are given the length of the
hypotenuse, you can determine the length of a
side by dividing it by_________________________ __
_________________________.
l v2
v2, then rationalizing the denominator, when
necessary.
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EXAMPLES Find the length of the hypotenuse
in each isosceles triangle below.
3v2
4v2
5v2
6v2
7v2
12v2
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Recall Triangle Inequalities

• If two angles of a triangle are not congruent,
  then the longest side lies opposite the _______
  angle and the shortest side lies opposite the
  ________ angle.

largest
smallest
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30-60-90 TRIANGLE THEOREM
30-60-90 TRIANGLE THEOREM In a 30-60-90
triangle, if the side opposite the 30 degree
angle has length, l, the hypotenuse has
length _______. NOTE These triangles are
sometimes referred to as 1-2-v3 right
triangles.
2l
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Easy way to remember the relationship among
angles and sides in 30-60-90 triangles

• 1. Rank order the following numbers from
  smallest to largest
• 1, 2, v3
• 2. Now, use the Triangle
• Inequality Theorem to
• place the side
• lengths 1l, v3l , 2l
• opposite the
• appropriate angles in a
• 30-60-90 triangle.

60
2l
1l
1, v3 , 2
30
lv3
NOTE It is usually easier to determine the
length of the shortest and longest sides,
initially.
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Find the length of each indicated side
60
____
____
30
____
NOTE The length of one side will be provided by
your instructor.
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Find the length of each indicated side.
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In summary
Pythagorean Primitives 3 4 5 5 12 13 8
15 17 7 24 25
and their multiples!

• We can find the lengths of sides in right
  triangles by using

c a
b Pythagorean Theorem c2 a2 b2
30-60-90 ? 30 2l lv3
60 l
45-45-90 ? l
45 l lv2 45
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Putting it all together
Find the length of each indicated side.
20v3
8 __ __
5 40
20
8 3
8 4
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Homework Assignment

• Special Right Triangles WS (1-10 all, 12)