Download Similar Triangles

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MFM 2P TEST
Similar Triangles
KU
APP
COM
Total
31
15
Level
46
Communication is a level mark based on how clearly the steps to solving a problem are laid out, and/or how clearly you explain an answer.
Curriculum Expectation Met
MT.1 use their knowledge of ratio and proportion to investigate similar triangles and solve problems
related to similarity;
1. True or False. Clearly write the letter T or F beside each statement. If it is unclear
which letter you have written, the question will be marked wrong.
a. ______ Similar triangles are the same size and shape.
b. ______ Congruent triangles have equal side lengths.
c. ______ Similar triangles have equal angles and side lengths in proportion.
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d. ______ The side across from the right angle is called the hypotenuse.
e. ______ To determine if two triangles are similar, you can use ASA rule.
2. Put a checkmark beside the two ways to recognize if two triangles are similar.
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_____
Side lengths are equal.
_____
Corresponding angles are equal.
_____
Ratio of corresponding side lengths are equal.
_____
Corresponding angles add to 180.
3. Complete the sentences, using the word bank provided. You may need to use words
more than once.
Word Bank:
complimentary, congruent, equal, right, similar, supplementary, triangle, SAS
a. All 3 angles in a _______________________ add up to 180.
b. If two objects are the same shape and size, they are said to be
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___________________.
c. ___________________ triangles have ____________________ angles and
corresponding side lengths with equivalent ratios.
d. The Pythagorean Theorem can only be applied to _____________ triangles.
e. ______________________ angles add up to 180.
f.
______________________ angles add up to 90.
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g. One way to show two triangles are similar is to have _____________________.
4. Use the Pythagorean Theorem to calculate the length of the third side of the right
angled triangle. a2 + b2 = c2
9 cm
13 cm
c
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13 m
12 m
a
5. Determine the angle measure indicated by each measure. Explain how you
know (e.g. complementary angles, or the angles in a triangle add up _____).
w = ______
Reason:
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3
m = ______
n = ______
n
Reason:
6. Set-up proportions and solve for the missing side length(s) in each diagram.
a.
T
8
A
C
6
10
25
x
B
∆ABC ~ ∆VTU
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b.
V
y
U
4
P
N
y
14
9
5
Q
R
M
12
x
Write a similar triangle statement for the triangles in part b.
∆________ ~ _________
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7. State if the triangles in each pair are similar (SIMILAR or NOT SIMILAR).
If they are similar, show the ratio of side lengths and state any equal
angles then complete the similarity statement.
Diagram
Similarity Statement (complete only if they are
similar)
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Ratio of Sides or
Equal Angles
SIMILAR
(AA, SSS, or SAS)
or
NOT SIMILAR
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8.
A tree is 3.8 m high. It casts a shadow 1.6 m long. A nearby flagpole casts a
shadow 5.2 m long. What is the height of the flagpole? Draw a beautiful
diagram of the situation.
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9. Triangle ABC and MNP are similar. The lengths of the sides of triangle ABC are 22,
25 and 34. The shortest side of triangle MNP is 108. What is the perimeter of
triangle MNP? [Hint: draw a diagram of two similar triangles and label all the sides
you know first. I have given two similar triangles below to help you get started.]
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Bonus – What is the name of the awesome educational assistant that helps us
with our work every day?