Applying Special Right Triangles 5-8 Applying Special Right Triangles Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

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. 4.

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

45-45-90 Investigation Materials: Ruler Group member 1: 1” lines Using a line on your notebook paper and the margin line, draw a ___” vertical line and a ___” horizontal line. (make a right angle) Draw the hypotenuse. Find the length of the hypotenuse using the Pythagorean theorem. Write a conclusion of your findings.

Formulas!  Leg = Leg Hypotenuse = Leg√2

Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form.

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.

Check It Out! Example 1a Find the value of x. Give your answer in simplest radical form. x = 20 Simplify.

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

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.

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.

Day 1 Assignment P 360 1-3, 9 - 12

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”

Formulas Long Leg = Short Leg √3 Hypotenuse = Short Leg ∙ 2

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.

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

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

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.

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.

Example 4 Continued Step 2 Find the length x of the shorter leg. 6 = 2x Hypotenuse = 2(shorter leg) 3 = x Divide both sides by 2. Step 3 Find the length h of the longer leg. The pin is approximately 5.2 centimeters high. So the fastener will fit.

Lesson Quiz: Part I Find the values of the variables. Give your answers in simplest radical form. 1. 2. 3. 4. x = 10; y = 20

Worksheet 