5-8 Applying Special Right Triangles Chapter 5 5-8 Applying Special Right Triangles

Objectives Justify and apply properties of 45°-45°-90° triangles.

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.

Special right 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.

Triangle theorem

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

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

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

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.

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

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

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

Application An ornamental pin is in the shape of an equilateral triangle. The length of each side is 6 centimeters. Josh will attach the fastener to the back along AB. Will the fastener fit if it is 4 centimeters long?

Application What if…? A manufacturer wants to make a larger clock with a height of 30 centimeters. What is the length of each side of the frame? Round to the nearest tenth.

Student Guided Practice Do problems 1-8 in your book page372

Homework Do problems 9-16 in your book page 372

Closure Today we learned about special right triangles Next class we are going to learned about properties and attributes of polygons