This document provides instruction on similarity in right triangles. It defines similarity and introduces Theorem 7-3, which states that if two right triangles have corresponding angles that are congruent, then the triangles are similar. The document also presents two corollaries to Theorem 7-3: 1) the length of the altitude to the hypotenuse is the geometric mean of the hypotenuse segments, and 2) the length of each leg is the geometric mean of the hypotenuse and adjacent hypotenuse segment. Examples are provided to illustrate the corollaries. The document concludes with practice problems finding geometric means and identifying corresponding parts of similar right triangles.

1. Unit 7.4 Similarity in Right Triangles
Learning Goal: To find and use relationships in
similar right triangles

2. Warm-Up
ΔDAC
ΔDCB ΔCAB

8. Corollary 1 to Theorem 7-3
• Corollary
The length of the altitude to the
If… C
hypotenuse of a right triangle is
the geometric mean of the lengths
of the segments of the hypotenuse.
A D B
Then…
Example
2 AD = CD
CD DB
8
Segments of 2 4 Altitude to
4 hypotenuse = hypotenuse
4 8

9. Corollary 2 to Theorem 7-3
• Corollary
The altitude to the hypotenuse of a
right triangle separates the hypotenuse If… C
so that the length of each leg of the
triangle is the geometric mean of the
length of the hypotenuse and the length
A D B
of the segment of the hypotenuse
adjacent to the leg. Then…
Example AB = AC and AB = CB
AC AD CB DB
1 4
Hypotenuse 4 2 Leg
=
2 2 1 Segment of
hypotenuse
adjacent to leg

10. Find the geometric mean for each pair of numbers.
1. 4 and 9 2. 3 and 18 3. 5 and 9
6 ≈7.3 ≈6.7
4. 9 and 16 5. 5 and 80 6. 8 and 32
12 20 16
Find the value of the variables.
13. 8.
x≈8.4
x≈2.2 y≈4.6
y=2 z≈5.5
z≈4.5
9. 10.
x=65 x=6
y=60 y≈4.5
z=156 z≈6.7

11. LEARNING GOALS SCALE - Unit 7-4: Similarity in Right Triangles
•Students will be able to identify corresponding parts of similar right triangles.
•Students will understand and be able to understand Theorem 7-3 and its corollaries.
SCORE LEARNING GOALS ACHIEVED
“I CAN TEACH IT!”
4 •I am able to identify similar right triangles.
•I understand and can use Theorem 7-3.
•I understand and can use the Corollaries to Theorem 7-3.
•I answered all practice questions correctly.
•I am able to help other students achieve the learning goals.
“GOT IT…Yes!”
3 •I am able to identify similar right triangles.
•I understand or can use Theorem 7-3.
•I understand or can use the Corollaries to Theorem 7-3.
•I answered 8 or 9 practice questions correctly.
“ALMOST! Yes, but…”
2 •I am able to identify similar right triangles.
•I understand Theorem 7-3.
•I understand the Corollaries to Theorem 7-3.
•I answered 6 or 7 practice questions correctly.
“GETTING THERE….No, but…”
1 •I am able to identify similar right triangles.
•I answered 5 practice questions correctly.
“CLUELESS… No idea”
0 •I have NO idea what you are talking about.
•“WHAT????”
•I answered fewer than 5 practice questions correctly.

12. We’re done.
(Except…)

13. Pages 464-465
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