Class Greeting

Objective: The students will solve problems using Special Right Triangles.

Special Right Triangles Chapter 8 – Lesson 3 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.

Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of 8.

Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. Rationalize the denominator.

Check It Out! Example 1a Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the angles are 45°-45°-90° x = 20 Simplify.

Check It Out! Example 1b Find the value of x. Give your answer in simplest radical form. Rationalize the denominator.

A 30°-60°-90° triangle is another special right triangle A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

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. 22 = 2x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x.

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. Rationalize the denominator. y = 2x Hypotenuse = 2(shorter leg). Substitute . Simplify.

Check It Out! Example 3a Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27 Substitute for x.

Check It Out! Example 3b Find the values of x and y. Give your answers in simplest radical form. y = 2(5) y = 10 Simplify.

Check It Out! Example 3c Find the values of x and y. Give your answers in simplest radical form. 24 = 2x Hypotenuse = 2(shorter leg) 12 = x Divide both sides by 2. Substitute 12 for x.

Check It Out! Example 3d Find the values of x and y. Give your answers in simplest radical form. Rationalize the denominator. x = 2y Hypotenuse = 2(shorter leg) Simplify.

Kahoot!

Lesson Summary: Objective: The students will solve problems using Special Right Triangles.

Preview of the Next Lesson: Objective: The students will be able to find the sine, cosine, and tangent of an acute angle and use trigonometric ratios to find side lengths in right triangles.

Stand Up Please