1. Similarity in Right Triangles
8-1
Similarity in Right Triangles
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry

2. Warm Up 1. Write a similarity statement comparing the two triangles.
Simplify.
Solve each equation.
x2 = 50
∆ADB ~ ∆EDC ±5

3. Objectives
Use geometric mean to find segment lengths in right triangles.
Apply similarity relationships in right triangles to solve problems.

4. Vocabulary
geometric mean

5. In a right triangle, an altitude drawn from the vertex of the right angle to the hypotenuse forms two right triangles.

6. Note 63

7. Example 1: Identifying Similar Right Triangles
Write a similarity statement comparing the three triangles.

8. Consider the proportion
Consider the proportion In this case, the means of the proportion are the same number, and that number is the geometric mean of the extremes.
The geometric mean of two positive numbers is the positive square root of their product. So the geometric mean of a and b is the positive number x such
that , or x2 = ab.

9. Example 2A: Finding Geometric Means
Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
4 and 25

10. Example 2B: Finding Geometric Means
Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
5 and 30

11. Example 3: Finding Side Lengths in Right Triangles
Find x, y, and z.

12. Check It Out! Example 3
Find u, v, and w.

13. 1. Write a similarity statement comparing the three triangles.
Exit Slip
For Items 1–3, use ∆RST.
1. Write a similarity statement comparing the three triangles.
2. If PS = 6 and PT = 9, find PR.
3. If TP = 24 and PR = 6, find RS.
(Leave your answer in simplest radical form)
∆RST ~ ∆RPS ~ ∆SPT 4