1. Class Greeting

2. Proving Similar Triangles
Chapter 7 – Lesson 3
Proving Similar Triangles

3. Objective: The students will be able to solve problems and prove triangles similar by using SSS~, and SAS~.

5. Verify that the triangles are similar.
Example 1: Verifying Triangle Similarity
Verify that the triangles are similar.
∆PQR and ∆STU
Therefore ∆PQR ~ ∆STU by SSS~.

7. Verify that the triangles are similar.
Example 2: Verifying Triangle Similarity
Verify that the triangles are similar.
∆DEF and ∆HJK
H  D
def.  angles
Therefore ∆DEF ~ ∆HJK by SAS~.

8. Example 3: Writing Proofs with Similar Triangles
Given: 3UT = 5RT and 3VT = 5ST
Prove: ∆UVT ~ ∆RST
Statements
Reasons
1. 3UT = 5RT;
3VT = 5ST
1. Given 2.
and
2. Division 3. 3.
Substitution 4.
RTS  VTU 4.
Vert. s Thm. 5.
∆UVT ~ ∆RST 5.
SAS ~

9. Example 4: Proving Triangles Are Similar
Given: E(–2, –6), F(–3, –2), G(2, –2), H(–4, 2), and J(6, 2).
Prove: ∆EHJ ~ ∆EFG by SAS~.
Step 1 Plot the points and draw the triangles.
Step 2 Use the Distance Formula to find the side lengths.
The scale factor is 2:1.

10. Step 3 Find the scale factor.
Example 4 Continued
Step 3 Find the scale factor.
= 2
= 2
Since and E  E, by the Reflexive Property, ∆EHJ ~ ∆EFG by SAS ~ .

11. Your Turn
Graph the image of ∆ABC after a dilation with scale factor
Verify that ∆A'B'C' ~ ∆ABC.
Step 1 Multiply each coordinate by to find the coordinates of the vertices of ∆A’B’C’.
Step 2 Graph ∆A’B’C’.

12. Step 2 Graph ∆A’B’C’.
B’ (2, 4)
A’ (0, 2)
C’ (4, 0)

13. Step 3 Use the Distance Formula to find the side lengths.
The scale factor is 2:3.

14. Step 4 Find the scale factor.
Since , ∆ABC ~ ∆A’B’C’ by SSS ~.

15. Kahoot!

16. Lesson Summary:
Objective: The students will be able to solve problems and prove triangles similar by using SSS~, and SAS~.

17. Preview of the Next Lesson:
Objective: The students will review for Lesson 7-1 to 7-4 test.

18. Stand Up Please