2. 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

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

4. 45°-45°-90° Triangles
ΔABC and ΔPQR are 45°-45°-90° triangles. Find the length of the hypotenuse in ΔPQR.
Example 1

5. 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 inches.
Example 1

6. 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

7. Key Concept 1

8. 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

9. 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 = in., y = 8 in.
Example 2

10. 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

11. Key Concept 3

12. 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

13. 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

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

15. 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 in.
B in.
C in.
D. 32 in.
Example 3 CYP