1. Warm-up
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2. WALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 45°-45°-90° triangle measures millimeters?
Example 3-1a

3. The area of one of these triangles is or 24.5 millimeters.
The length of the hypotenuse of one 45°-45°-90° triangle is millimeters. The length of the hypotenuse is times as long as a leg. So, the length of each leg is 7 millimeters.
The area of one of these triangles is
or 24.5 millimeters.
Answer: Since there are 8 of these triangles in one square quadrant, the area of one of these squares is 8(24.5) or 196 mm2.
Example 3-1b

4. WALLPAPER TILING If each 45°-45°-90° triangle in the figure has a hypotenuse of millimeters, what is the perimeter of the entire square?
Answer: 80 mm
Example 3-1c

5. Find a.
The length of the hypotenuse of a 45°-45°-90° triangle is times as long as a leg of the triangle.
Example 3-2a

6. Rationalize the denominator.
Divide each side by
Rationalize the denominator.
Multiply.
Divide.
Answer:
Example 3-2b

7. Find b.
Answer:
Example 3-2c

8. Find QR.
Example 3-3a

9. is the longer leg, is the shorter leg, and is the hypotenuse.
Multiply each side by 2.
Answer:
Example 3-3b

10. Find BC.
Answer: BC = 8 in.
Example 3-3c

11. COORDINATE GEOMETRY is a 30°-60°-90° triangle with right angle X and as the longer leg. Graph points X(-2, 7) and Y(-7, 7), and locate point W in Quadrant III.
Example 3-4a

12. Graph X and Y. lies on a horizontal gridline of the coordinate plane
Graph X and Y lies on a horizontal gridline of the coordinate plane. Since will be perpendicular to it lies on a vertical gridline. Find the length of
Example 3-4b

13. is the shorter leg. is the longer leg. So, Use XY to find WX.
Point W has the same x-coordinate as X. W is located units below X.
Answer: The coordinates of W are or about
Example 3-4b

14. Answer: The coordinates of S are or about
COORDINATE GEOMETRY is at 30°-60°-90° triangle with right angle R and as the longer leg. Graph points T(3, 3) and R(3, 6) and locate point S in Quadrant III.
Answer: The coordinates of S are or about
Example 3-4d