5-8 Applying Special Right Triangles
For Exercises 1 and 2, find the value of x . Give your answer in simplest radical form.
1.
2.
3.
Tell if the measures 7, 11, and 15 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
Holt McDougal Geometry

5-8 Applying Special Right Triangles
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
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 1A: 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 1B: 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
Let’s try some more!
Example 1a
Find the value of x . Give your answer in simplest radical form.
Holt McDougal Geometry

5-8 Applying Special Right Triangles
Find the values of the variables. Give your answers in simplest radical form.
1.
2.
Find the perimeter and area of each figure. Give your answers in simplest radical form.
3.
a square with diagonal length 20 cm
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
Let’s try some more!
Example 3a
Find the values of x and y . Give your answers in simplest radical form.
Holt McDougal Geometry

5-8 Applying Special Right Triangles
Let’s try some more!
Example 3c
Find the values of x and y . Give your answers in simplest radical form.
Holt McDougal Geometry