Similar Right Triangles. Chapter 8. Cut an index card along one of its diagonals. On one of the right triangles, draw an altitude from the right angle to the hypotenuse. Cut along the altitude to form two right triangles.
On one of the right triangles, draw an altitude from the right angle to the hypotenuse. Cut along the altitude to form two right triangles.
You should now have three right triangles. Compare the triangles. What special property do they share? Explain.Activity: Investigating similar right triangles. Do in pairs or threes
∆CBD ~ ∆ABC, ∆ACD ~ ∆ABC, ∆CBD ~ ∆ACD
BUsing a geometric mean to solve problems
They ALL look the same!
Similar = same shape, different size
If you want to find the Altitude… use Geometric Mean
CD is the Geometric Mean
18 = x2
√18 = x
√9 ∙ √2 = x
3 √2 = x
Rotate the triangle to help visualize what part you need
√14 = yExample: Find y (the right leg of the triangle) using Geometric Mean
5 + 2
14 = y2
√245 = yExample: Find y (the left leg of the triangle) using Geometric Mean
245 = y2
7√5 = y
A. Identify the similar triangles.
B. Find the height h of the roof.Ex. 1: Finding the Height of a Roof
∆XYW ~ ∆YZW ~ ∆XZY.
Corresponding side lengths are in proportion.
6.3h = 5.5(3.1)
Cross Product property
Solve for unknown h.
The height of the roof is about 2.7 meters.