SUBJECT
Geometry
UNIT TITLE Similarity
Topic: 8-4 Similarity in Right Triangles
Objective:
To find and use relationships in similar right triangles
Core Content for Assessment:
MA-11-3.1.6 Students will apply the concepts of congruence and
similarity to solve real world problems
Materials/Resources:
Right Triangle Activity worksheet, calculators, index cards, scissors
Warm Up/Bell Ringer/Do Now:
Solve each proportion:
x 18
2 x
15 18



1.
2.
3.
8 24
3 7
4
x
4.
51 17

x 13
Procedures:
1. Warm Up
2. Check HW as appropriate
3. Investigation: Similarity in Right Triangles
4. Discuss theorem discovered from investigation
Thm: The altitude to the hypotenuse of a right triangle divides the
triangle into two triangles that are similar to the original triangle
and to each other.
5. Geometric Mean of a and b – the positive number x such that
a x
 -> x2 = ab -> x  ab
x b
6. Examples: Find the Geometric Mean
a. 4 and 25
4 and 18
4
x
4 x


x 25
x 18
X2=100
x2=72
X=10
x= 72 = 6 2
7. Corollary: The length of the altitude to the hypotenuse of a right
triangle is the geometric mean of the lengths of the segment of
the hypotenuse.
a x

x b
X
a
b
ex. Find x:
a. a=3 b=27
b. a=5 b=25
8. Corollary: The altitude to the hypotenuse of a right triangle
separates the hypotenuse so that the length of each leg of the
triangle is the geometric mean of the length of the adjacent
hypotenuse segment and the length of the hypotenuse.
x
x
a
b
a
x2=a(a+b)
b
x2=b(a+b)
ex. Solve for the variable
x
8
10
3
9
6
a
b
x
21
7
13
29
20
9. Class work as appropriate
a
b
Lesson Assessments:
Assign HW as appropriate
Class work check
Investigating Similar Right Triangles
1. Cut an index card along one of its diagonals.
2. On one of the right triangles mark the right
angle.
3. With the other right triangle fold in the
altitude. Cut this triangle down the altitude.
You should now have three right triangles.
4. Compare the 3 right triangles. What special
property do they share?