Example 1: 45°-45°-90° Triangles Key Concept: 45°-45°-90° Triangles

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Presentation transcript:

Example 1: 45°-45°-90° Triangles Key Concept: 45°-45°-90° Triangles Main Idea Example 1: 45°-45°-90° Triangles Key Concept: 45°-45°-90° Triangles Example 2: Find Missing Measures of a 30°-60°-90° Triangle Key Concept: 30°-60°-90° Triangles Example 3: Use Special Right Triangles Lesson Menu

Use special right triangles to solve problems. Main Idea/Vocabulary

45°-45°-90° Triangles ΔABC and ΔPQR are 45°-45°-90° triangles. Find the length of the hypotenuse in ΔPQR. Example 1

Multiply the length of AC by the scale factor, 6. 45°-45°-90° Triangles The scale factor from ΔABC to ΔXYZ is or 6. Use the scale factor to find the hypotenuse. Multiply the length of AC by the scale factor, 6. Answer: So, the hypotenuse of ΔPQR measures 6 inches. Example 1

Triangle ABC and triangle PQR are 45°-45°-90° triangles Triangle ABC and triangle PQR are 45°-45°-90° triangles. Find the length of the hypotenuse in triangle PQR. A. B. C. D. Example 1 CYP

Key Concept 1

Find Missing Measures of a 30°-60°-90° Triangle Triangle ABC and triangle XYZ are 30°-60°-90° triangles. Find the exact length of the missing measures. Example 2

Find Missing Measures of a 30°-60°-90° Triangle The scale factor from ΔABC to ΔXYZ is 4. Use the scale factor to find the missing measures. y = 2 • 4 or 8 Multiply the length of AB by the scale factor. So, y is 8 inches. Multiply the length of AC by the scale factor. So, x is inches. Answer: x = 4 in., y = 8 in. Example 2

Triangle ABC and triangle XYZ are 30°-60°-90° triangles Triangle ABC and triangle XYZ are 30°-60°-90° triangles. Find the exact length of the missing measures. A. B. C. D. Example 2 CYP

Key Concept 3

Use Special Right Triangles PACKAGING The height of a box lid measures 20 inches. A ribbon glued along its diagonal measures 40 inches. What is the length of the base? Round to the nearest tenth. Example 3

Use Special Right Triangles The triangle shown is a 30°-60°-90° triangle. The longer leg of a 30°-60°-90° triangle is times the length of the shorter leg. longer leg = shorter leg • Relationship between sides Substitute. Example 3

Use Special Right Triangles This is a real-world situation. Use a calculator to find the decimal approximation of the length. 20 3 34.64101615 ENTER × 2nd [ ] Round to the nearest tenth. Answer: The length of the base of the package is about 34.6 inches long. Example 3

SEWING A 16-inch square pillow has a diagonal ribbon sewn across it SEWING A 16-inch square pillow has a diagonal ribbon sewn across it. Find the length of the diagonal ribbon. Round to the nearest tenth. A. 13.9 in. B. 22.6 in. C. 27.7 in. D. 32 in. Example 3 CYP