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5-8

5-8. Applying Special Right Triangles. Warm Up. Lesson Presentation. Lesson Quiz. 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.

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5-8

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  1. 5-8 Applying Special Right Triangles Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. 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.

  3. Objectives Justify and apply properties of 45°-45°-90° triangles. Justify and apply properties of 30°- 60°- 90° triangles.

  4. Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of 8.

  5. Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 5. Rationalize the denominator.

  6. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of Check It Out! Example 1a Find the value of x. Give your answer in simplest radical form. Simplify. x = 20

  7. Check It Out! Example 1b Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 16. Rationalize the denominator.

  8. 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.

  9. A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

  10. 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. 22 = 2x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x.

  11. 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. Rationalize the denominator. y = 2x Hypotenuse = 2(shorter leg). Simplify.

  12. Substitute for x. Check It Out! Example 3a Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

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