9.2 Special Right Triangles

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Presentation transcript:

9.2 Special Right Triangles 45-45-90 30-60-90

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. Find the value of x. Give your answer in simplest radical form.

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

Example 2: Craft Application Jana is cutting a square of material for a tablecloth. The table’s diagonal is 36 inches. She wants the diagonal of the tablecloth to be an extra 10 inches so it will hang over the edges of the table. What size square should Jana cut to make the tablecloth? Round to the nearest inch.

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. Find the values of x and y. Give your answers in simplest radical form.

Check It Out! Example 3a Find the values of x and y. Give your answers in simplest radical form. Find the values of x and y. Give your answers in simplest radical form.

Lesson Quiz: Part I Find the values of the variables. Give your answers in simplest radical form. 1. 2. 3. 4.

Lesson Quiz: Part II Find the perimeter and area of each figure. Give your answers in simplest radical form. 5. a square with diagonal length 20 cm 6. an equilateral triangle with height 24 in.* 7. HONORS: For a circle with radius = r find P & A for inscribed or circumscribed squares and equilateral triangles