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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 Isosceles Right Triangle Theorem ... – PowerPoint PPT presentation

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Title: Lesson 7.3 Two Special Right Triangles


1
Lesson 7.3 Two Special Right Triangles
  • Objectives
  • To use properties of 45-45-90 triangles
  • To use properties of 30-60-90 triangles

2
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.
3
EXAMPLES Find the length of the hypotenuse
in each isosceles triangle below.
3v2
4v2
5v2
6v2
7v2
12v2
4
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
5
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
6
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.
7
Find the length of each indicated side
60
____
____
30
____
NOTE The length of one side will be provided by
your instructor.
8
Find the length of each indicated side.
9
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
10
Putting it all together
Find the length of each indicated side.
20v3
8 __ __
5 40
20
8 3
8 4
11
Homework Assignment
  • Special Right Triangles WS (1-10 all, 12)
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