1. SPECIAL RIGHT TRIANGLES
NOTES 9.7
SPECIAL RIGHT TRIANGLES

2. 30º-60º-90º Triangles
Theorem 72: In a triangle whose angles have the measures of 30º, 60º, and 90º, the lengths of the sides opposite these angles can be represented by x, , and 2x respectively. (30º-60º-90º-Triangle Theorem)
30º 2x
60º x

3. Find BC and AC. 10 x 2x = 10 Place x, , and 2x on the diagram.
60º B x

4. 45º-45º-90º Triangles
Theorem 73: In a triangle whose angles have the measures of 45º, 45º, and 90º, the lengths of the sides opposite these angles can be represented by x, x, and , respectively. (45º-45º-90º-Triangle Theorem) x
45º x
45º

5. MOPR is a square. Find MP. 9 x = 9 x
The diagonal divides the square into two 45º-45º-90º triangles.
Place x, x, and on the corresponding parts of the triangle.
Since x = 9,
MP = R M 9
x = 9 O P x

6. Find ST and TV.
Place x, x, and onto the diagram. T x S x 4 V
45º