5-8 Applying Special Right Triangles
Bellringer:
For Exercises 1 and 2, find the value of x.
Round your answers to the nearest tenth.
1.
Holt McDougal Geometry
2.
5-8 Applying Special Right Triangles
Objectives
Justify and apply properties of
45°-45°-90° triangles.
Justify and apply properties of
30°- 60°- 90° triangles.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Remember!
By the Triangle Inequality Theorem, the
sum of any two side lengths of a triangle is
greater than the third side length.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
You can also use side lengths to classify a
triangle as acute or obtuse.
B
c
A
Holt McDougal Geometry
a
b
C
5-8 Applying Special Right Triangles
Example 1: Classifying Triangles
Tell if the measures can be the side lengths
of a triangle. If so, classify the triangle as
acute, obtuse, or right.
5, 7, 10
Holt McDougal Geometry
5-8 Applying Special Right Triangles
A diagonal of a square divides it into two congruent
isosceles right triangles. Since the base angles of an
isosceles triangle are congruent, the measure of
each acute angle is 45°. So another name for an
isosceles right triangle is a 45°-45°-90° triangle.
A 45°-45°-90° triangle is one type of special right
triangle. You can use the Pythagorean Theorem to
find a relationship among the side lengths of a 45°45°-90° triangle.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Example 2A: Finding Side Lengths in a 45°- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Example 2B: Finding Side Lengths in a 45º- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
A 30°-60°-90° triangle is another special right
triangle. You can use an equilateral triangle to find
a relationship between its side lengths.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Example 3A: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y.
Give your answers in
simplest radical form.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Example 3B: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y. Give
your answers in simplest
radical form.
Holt McDougal Geometry
5-8 Applying Special Right Triangles
Example 3C: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y. Give your
answers in simplest radical form.
Holt McDougal Geometry