Warm-up Page 354 (12-24) even.

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Warm-up Page 354 (12-24) even

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

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

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

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

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

Find b. Answer: Example 3-2c

Find QR. Example 3-3a

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

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

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

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

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

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