Presentation On Theme: 73 Special Right Triangles Presentation Transcript:
1 7.3 Special Right Triangles
2 Objectives Use properties of 45° – 45° – 90° triangles
3 Side Lengths of Special Right sRight triangles whose angle measures are 45° – 45° – 90° or 30° – 60° – 90° are called special right triangles. The theorems that describe the relationships between the side lengths of each of these special right triangles are as follows:
4 45° – 45° – 90°Theorem 7.6In a 45°- 45°- 90° triangle, the length of the hypotenuse is 2 times the length of a leg.hypotenuse = 2 leg45 °x245 °
5 Example 1: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?
6 Example 1: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 isor 24.5 millimeters.Answer: Since there are 8 of these triangles in one square quadrant, the area of one of these squares is 8 or 196 mm2.
7 Your Turn: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
8 Example 2:Find a.The length of the hypotenuse of a 45°- 45°- 90° triangle is times as long as a leg of the triangle.
9 Example 2: Divide each side by Rationalize the denominator. Multiply.Answer: