Holt McDougal Geometry

5-8 Applying Special Right Triangles5-8 Applying Special Right Triangles

Holt Geometry

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Holt McDougal Geometry

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Warm UpFor Exercises 1 and 2, find the value of x. Give your answer in simplest radical form.

1. 2.

Simplify each expression.

3. 4.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

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

Justify and apply properties of 30°- 60°- 90° triangles.

Objectives

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Materials: RulerGroup member 1: 1” linesGroup member 2: 2”linesGroup member 3: 3”linesGroup member 4: 4”lines

1)Using a line on your notebook paper and the margin line, draw a ___” vertical line and a ___” horizontal line. (make a right angle)2)Draw the hypotenuse. Find the length of the hypotenuse using the Pythagorean theorem.3)Write a conclusion of your findings.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle

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

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle

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

Rationalize the denominator.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! Example 1a

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

x = 20 Simplify.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! Example 1b

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

Rationalize the denominator.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

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.

Jana needs a 45°-45°-90° triangle with a hypotenuse of 36 + 10 = 46 inches.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! 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.

Tessa needs a 45°-45°-90° triangle with a hypotenuse of 42 cm.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Day 1 Assignment• P 360 1-3, 9 - 12

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Investigation• Materials: Ruler, Protractor

Draw a 1” line beginning at the vertical line on a blue horizontal line

From the end of the 1” line measure 60º. Draw to the vertical margin line.

Measure hypotenuse with ruler. Round to nearest whole number.

Use Pythagorean Theorem to find the other leg.

Repeat in groups. Member 1: 2”

Member 2: 3”

Member 3: 4”

Member 4: 5”

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Formulas

Hypotenuse = Short Leg ∙ 2

Long Leg = Short Leg √3

Holt McDougal Geometry

5-8 Applying Special Right Triangles

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.Hypotenuse = 2(shorter leg)

22 = 2x

11 = x

Substitute 11 for x.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

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.

Hypotenuse = 2(shorter leg).y = 2x

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! Example 3a

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

Hypotenuse = 2(shorter leg)

y = 27

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! Example 3b

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

Simplify.

y = 2(5)

y = 10

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! Example 3c

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

Hypotenuse = 2(shorter leg)

Divide both sides by 2.

Substitute 12 for x.

24 = 2x

12 = x

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Check It Out! Example 3d

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

Rationalize the denominator.

Hypotenuse = 2(shorter leg)x = 2y

Simplify.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Example 4: Using the 30º-60º-90º Triangle Theorem

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?

Step 1 The equilateral triangle is divided into two 30°-60°-90° triangles.

The height of the triangle is the length of the longer leg.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Example 4 Continued

Step 2 Find the length x of the shorter leg.

Step 3 Find the length h of the longer leg.

The pin is approximately 5.2 centimeters high. So the fastener will fit.

Hypotenuse = 2(shorter leg)6 = 2x

3 = x Divide both sides by 2.

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Lesson Quiz: Part IFind the values of the variables. Give your answers in simplest radical form.

1. 2.

3. 4.

x = 10; y = 20

Holt McDougal Geometry

5-8 Applying Special Right Triangles

Worksheet