1. Bellwork
Determine whether the triangles are similar. A B

2. Bellwork The triangles are similar. Find the values of x and y. A B C
A. x = 5.5, y = 12.9
B. x = 8.5, y = 9.5
C. x = 5, y = 7.5
D. x = 9.5, y = 8.5 A B C D

3. Unit 5 Lesson 2 Triangle Similarity
Honors Geometry
Unit 5 Lesson 2
Triangle Similarity

4. Similar Triangles
Showing that triangles are similar is very much like showing that they are congruent
We will use “shortcuts”
A special combination of congruent angles and proportional sides
There are 3 shortcuts

5. First,
Keep in mind, if two angles from the triangles are congruent, what must be true about the third?
Notice the similarity statement!

6. Next
Notice the sides are proportional, not congruent!

7. Finally,
The congruent angles must be between the proportional sides!

8. Similar Triangles?
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
ΔQXP ~ ΔNXM by AA Similarity.

9. Similar Triangles?
Determine whether the triangles are similar. If so, write a similarity statement.
A. Yes; ΔABC ~ ΔFGH
B. Yes; ΔABC ~ ΔGFH
C. Yes; ΔABC ~ ΔHFG
D. No; the triangles are not similar. A B C D

10. Similar Triangles?
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
By the Reflexive Property, M  M.
ΔMNP ~ ΔMRS by the SAS Similarity Theorem.

11. Determine whether the triangles are similar
Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.
A. ΔAFE ~ ΔABC by SSS Similarity Theorem
B. ΔAFE ~ ΔACB by SSS Similarity Theorem
C. ΔAFE ~ ΔAFC by SSS Similarity Theorem
D Not Similar A B C D

12. Determine whether the triangles are similar
Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.
A. ΔPQR ~ ΔSTR by SSS Similarity Theorem
B. ΔPQR ~ ΔSTR by SAS Similarity Theorem
C. ΔPQR ~ ΔSTR by AAA Similarity Theorem
D. The triangles are not similar. A B C D

13. Given ΔABC and ΔDEC, which of the following would be sufficient information to prove the triangles are similar?
A =
B. mA = 2mD
C =
D =
___ AC DC __ 4 3 BC 5 EC A B C D

14. Use Similar Triangles to Solve using proportion
ALGEBRA Given , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.
Answer: RQ = 8; QT = 20

15. ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC.

16. Within One Triangle… Similarity can exist inside of a triangle
Proportional Parts…
Special Segments
Midsegments

17. A Segment Parallel to one side
This segment can be drawn parallel to any one of the three sides

18. Find the Length of a Side

19. Midsegment
The midsegment is half the length of the side that its parallel to

20. Use the Triangle Midsegment Theorem
In the figure, DE and EF are midsegments of ΔABC. Find AB.
ED = 1/2 AB
5 = 1/2 AB
10 = AB

21. A B C D In the figure, DE and DF are midsegments of ΔABC. Find BC.

22. A B C D In the figure, DE and DF are midsegments of ΔABC. Find DE.

23. No triangle at all…
The same ratio is cut into every transversal

24. Use Proportional Segments of Transversals
MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.

25. In the figure, Davis, Broad, and Main Streets are all parallel
In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x.
A. 4
B. 5
C. 6
D. 7 A B C D