Warm Up
For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form.
1. 2.
Simplify each expression.
3.
𝟏𝟐
√𝟑
4.
√𝟐𝟎
𝟐
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Geometry/Lesson 5-8: Applying Special Right Triangles
Objectives:
 Justify and apply properties of 45°-45°-90° triangles.
 Justify and apply properties of 30°- 60°- 90° 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.
1

Example 1: Find the value of x. Give your answer in simplest radical form.
A.
B.
C.I.O.-Example 1: Find the value of x. Give your answer in simplest radical form. b.
a.
Example 2:
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.
2

A.
C.I.O.-Example 2:
What if...? Tessa’s other dog is wearing a square bandana with a side length of 42 cm. What would you expect the circumference of the other dog’s neck to be? Round to the nearest centimeter.
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 3: Find the values of x and y. Give your answers in simplest radical form.
B.
3

C.I.O.-Example 3: Find the values of x and y. Give your answers in simplest radical form. b.
a. c.
d.
Example 4:
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?
4

3.
C.I.O.-Example 4:
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.
Lesson Quiz: Part I
Find the values of the variables. Give your answers in simplest radical form.
1. 2.
4.
5

Lesson Quiz: Part II
Find the perimeter and area of each figure. Give your answers in simplest radical form. a square with diagonal length 20 cm 6. an equilateral triangle with height 24 in. 5. p. 372: 9-15, 17-21, 25, 27, 29
10) 12) 14)
6