1. 8.5 Proving Triangles are Similar
Unit IIA Day 6

2. Do Now Explain how to use the SSS Similarity Theorem.
Explain how to use the SAS Similarity Theorem.
Are the triangles below similar? How do you know?

3. Reminder:
Geometry in the real world!

4. Ex. 2A Which of the following triangles are similar? How do you know?
KML and QSR; by SSS ~

5. Ex. 3A: Using the SAS Similarity Thm.
In the figure AC = 6, AD = 10, BC = 9, and BE = 15.
Is ΔACB ~ ΔDCE? Explain.
By subtraction, you can find that DC = 4 and EC = 9. Corresponding sides are proportional (ratio 2:3). Also, <ACB and <DCE are vertical angles. So the triangles are similar by SAS Similarity Theorem.

6. Ex. 4A Find the value of x that makes ∆ABC ~ ∆DEF .
Then find all side lengths.
x = 7
BC = 6, DF = 24

7. Ex. 5: Finding Indirect Distance
Due to the reflective property of mirrors, you can reason that <ACB = <ECD (angle of incidence = angle of reflection).
Using the fact that ∆ABC and ∆EDC are right triangles, you can apply the AA Similarity Postulate to conclude that these two triangles are similar.
DE/BA = EC/AC
x/5 = 85/6.5
x = ft

8. Ex. 6: Using Similar Triangles in Real Life
To measure the width of a river, you use a surveying technique, as shown in the diagram. Use the given lengths (in feet) to find RQ.
First of all, is ∆PQR ~ ∆STR?
The triangles are similar by AA Similarity Post.
Write the proportion PQ/ST = RQ/RT
63/9 = x/12
RQ = 84 ft.

9. Closure State the two similarity theorems presented in this lesson.
Sample answer: The SSS Similarity Theorem states that two triangles are similar if their corresponding sides are proportional. The SAS Similarity Theorem states that two triangles are similar if one angle is congruent, and the sides including these angles are proportional.