Download Similarity assessment REVIEW_key

Name ___________________________
Similarity Review
I can use the definition of similarity in terms of transformations to determine if two
figures are similar.
1.
Is triangle ABC similar to triangle DEC? Explain your reasoning using both your knowledge of
sides and angles. Show your work.
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2.
For each statement, decide whether you agree or disagree with it and explain your reasoning.
Statement
All rectangles are similar.
All triangles are similar.
When I enlarge a geometric
figure by a ratio of 2, both
the sides and angles
double in size.
True False Explain your reasoning
3.
Which of the following diagrams contains similar triangles? How do you know they are similar?
Similar Not
Similar
Is triangle BAC ~ triangle EDF?
Do Not assume angles are congruent unless
marked.
Is triangle ABC ~ triangle XYZ?
DE || BC
Is triangle ABC~ triangle ADE
Explain your reasoning (make sure you state a
theorem/postulate and support sides with ratios)
4.
A
Use the diagram below to answer the questions.
B
C
D
a) Which of the above four triangles is similar? The triangles that are similar are ________________
because__________________________________________________________________________
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(Remember to mention both sides and angles!)
b) On the grid, draw a triangle that is similar to one of the triangles but not congruent to any of them.
c) Now complete the following statement:
The triangle I drew is similar to triangle ________. I know this because (Think about scale factor)
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5. Which of the following figures are similar? (Note that angle marks do not indicate congruent angles
in this problem). Explain your reasoning.
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I can use congruence and similarity to solve problems.
6. A girl is 4ft 6in tall casts a shadow that is 8 ft. 6 in. long. The end of her shadow coincides with the
end of the shadow cast by a building 140ft from the girl. Find the height of the building. Explain or
show how you found your answer. DRAW A PICTURE. Round your answer to the nearest tenth of a
foot.
7. A family picture is 4”(width) by 6”(length). You want to enlarge the picture so that the new length is
14”. What will the new width be of the enlarged photo? Draw a picture. Show your work. Round your
answer to the nearest tenth of an inch.
8. A flagpole casts a 10 foot shadow. At the same time a 15 ft tree casts a 28 foot shadow. How tall
is the pole? Draw a picture. Show your work. Round your answer to the nearest tenth of a foot.
9. The width of a photo is 3” and the length is 5”. The new photo needs to be 7” in width. What will
be the length of the enlarged photo?
10. Given that the following triangles are similar, decide on a similarity ratio of the larger triangle to
the smaller triangle and then assign values in the picture such that the x=16. Solve the problem
showing that your problem works. Note that the picture is not necessarily to scale.
Similarity Ratio of ABC to DEF _________
AB = _____
BC = _____
EF = _____
Solve your problem and show x = 16
11. Solve for AD
I can prove theorems about triangles.
12. Complete the following proof given the picture below.
Given: DEǁAC
Prove: BAC ~ BDE
Statements
1.
2. B  B
3.
4.
Justifications
1.
2.
3. Corresponding Angles are Congruent
4.