http://www.ck12.org Chapter 7. Similarity
Vocabulary
Two triangles aresimilarif all their corresponding angles arecongruent(exactly the same) and their corresponding
sides areproportional(in the same ratio).
Guided Practice
Are the following triangles similar? If so, write a similarity statement.
Answers:
- Yes, 4 DGE∼4F GD∼4F DE.
- Yes, 4 HLI∼4HMJ.
- No, though^6 MNQ∼=^6 ONPbecause they are vertical angles, we need to have two pairs of congruent angles in
order to be able to say that the triangles are similar.
Practice
Use the diagram to complete each statement.
1. 4 SAM∼4
2. SA? =SM? =RI?
3.SM=
4.T R=
5.^9 ?=? 8
Answer questions 6-9 about trapezoidABCD.
- Name two similar triangles. How do you know they are similar?
- Write a true proportion.
- Name two other triangles that might not
- IfAB= 10 ,AE= 7 ,andDC=22, findAC. Be careful!
10.WritingHow many angles need to be congruent to show that two triangles are similar? Why?
11.WritingHow do congruent triangles and similar triangles differ? How are they the same?
Use the triangles below for questions 12-15.
AB= 20 ,DE= 15 ,andBC=k.
- Are the two triangles similar? How do you know?
- Write an expression forF Ein terms ofk.
- IfF E=12, what isk?
- Fill in the blanks: If an acute angle of a triangle is congruent to an acute angle in another ____-
triangle, then the two triangles are .
Use the diagram below to answer questions 16-20.