Triangle Similarity: SSS and SAS — Quiz Answers

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1
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What other information is needed to prove that triangle cap f cap g cap e approximates triangle cap i cap j cap h by the SAS similarity theorem?

A
angle cap f is congruent to angle cap j
B
angle cap i is congruent to angle cap f
C
angle cap g is congruent to angle i
D
angle cap e is congruent to angle cap h
2
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To prove that the triangles are similar by the SSS similarity theorem, which other sides or angles should be used?

A
line segment cap m cap n and line segment cap q cap r
B
angle cap s is congruent to angle cap o
C
angle cap s is congruent to angle cap n
D
line segment cap m cap n and line segment cap s cap r
3

Which statement is true?

A
The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.
B
The given sides and angles cannot be used to show similarity by either the SSS or SAS similarity theorems.
C
The given sides and angles can be used to show similarity by the SAS similarity theorem only.
D
The given sides and angles can be used to show similarity by the SSS similarity theorem only.
5

Which ratio is also equal to the fraction with numerator cap r cap t and denominator cap r cap x and the fraction with numerator cap r cap s and denominator cap r cap y ?

A
the fraction with numerator cap s cap t and denominator cap y cap x
B
the fraction with numerator cap s cap y and denominator cap r cap y
C
the fraction with numerator cap x cap y and denominator cap t cap s
D
the fraction with numerator cap r cap x and denominator cap x cap t
8

To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that

A
angle cap i measures 60 degrees .
B
angle cap i measures 30 degrees .
C
angle cap j measures 60 degrees .
D
angle cap j measures 30 degrees .
10

How can the triangles be proven similar by the SSS similarity theorem?

A
Show that the ratios the fraction with numerator cap u cap v and denominator cap z cap y and the fraction with numerator cap w cap u and denominator cap z cap x are equivalent, and angle cap u is congruent to angle cap z .
B
Show that the ratios the fraction with numerator cap u cap v and denominator cap z cap y , the fraction with numerator cap w cap u and denominator cap z cap x , and the fraction with numerator cap w cap v and denominator cap x cap y are equivalent.
C
Show that the ratios the fraction with numerator cap u cap v and denominator cap x cap y comma the fraction with numerator cap w cap u and denominator cap z cap x comma ,the fraction with numerator mathrm cap w cap u and denominator mathrm cap z cap x, and the fraction with numerator cap w cap v and denominator cap z cap y are equivalent.
D
Show that the ratios the fraction with numerator cap u cap v and denominator cap x cap y and the fraction with numerator cap w cap v and denominator cap z cap y are equivalent, and angle cap v is congruent to angle cap y .
11

To prove that triangle cap l cap m cap n approximates triangle cap x cap y cap z by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that

A
cap l cap m is 4 units and cap x cap z is 6 units.
B
cap l cap m is 6 units and cap x cap z is 4 units.
C
cap l cap m is 3 units and cap x cap z is 5 units.
D
cap l cap m is 5 units and cap x cap z is 3 units.
12

Which would prove that triangle cap A cap b cap c approximates triangle cap x cap y cap z ? Choose two correct answers.

A
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap b cap c and denominator cap y cap z comma angle cap c is congruent to angle cap z
B
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap b cap c and denominator cap y cap z is equal to the fraction with numerator cap A cap c and denominator cap x cap z
C
the fraction with numerator cap b cap c and denominator cap x cap y is equal to the fraction with numerator cap b cap A and denominator cap z cap x comma angle cap c is congruent to angle cap x
D
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap A cap c and denominator cap y cap z is equal to the fraction with numerator cap b cap c and denominator cap x cap z
E
the fraction with numerator cap A cap c and denominator cap x cap z is equal to the fraction with numerator cap b cap A and denominator cap y cap x comma angle cap A is congruent to angle cap x
13

To prove that the triangles are similar by the SSS similarity theorem, which other sides or angles should be used?

A
angle cap s is congruent to angle cap o
B
line segment cap m cap n and line segment cap q cap r
C
line segment cap m cap n and line segment cap s cap r
D
angle cap s is congruent to angle cap n
15

To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that

A
angle cap j measures 60 degrees .
B
angle cap i measures 30 degrees .
C
angle cap j measures 30 degrees .
D
angle cap i measures 60 degrees .
20

What other information is needed to prove that triangle cap f cap g cap e approximates triangle cap i cap j cap h by the SAS similarity theorem?

A
angle cap i is congruent to angle cap f
B
angle cap f is congruent to angle cap j
C
angle cap e is congruent to angle cap h
D
angle cap g is congruent to angle i

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