Triangle Similarity: SSS and SAS

Which two statements are missing in steps 3 and 4?

A

angle cap x is congruent to angle cap c triangle cap A cap b cap c approximates triangle cap z cap y cap x by the SAS similarity theorem.

B

the fraction with numerator cap z cap x and denominator cap A cap c triangle cap A cap b cap c approximates triangle cap z cap y cap x by the SSS similarity theorem.

C

the fraction with numerator cap A cap c and denominator cap x cap y triangle cap A cap b cap c approximates triangle cap z cap y cap x by the SSS similarity theorem.

D

angle cap b is congruent to angle cap y triangle cap A cap b cap c approximates triangle cap z cap y cap x by the SAS similarity theorem.

42

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

A

angle cap j measures 30 degrees .

B

angle cap j measures 60 degrees .

C

angle cap i measures 30 degrees .

D

angle cap i measures 60 degrees .

43

Which statement is true?

A

The given sides and angles can be used to show similarity by the SAS similarity theorem only.

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 both the SSS and SAS similarity theorems.

D

The given sides and angles can be used to show similarity by the SSS similarity theorem only.

44

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 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.

C

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.

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 .

45

What value of x will make the triangles similar by the SSS similarity theorem?

A

1 point 5

B

67 point 5

C

20

D

30

46

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.

47

What value of x will make triangle cap o cap n cap m similar to triangle cap s cap r cap q by the SAS similarity theorem?

A

25

B

20

C

16

D

50

48

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 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

B

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

C

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

D

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

E

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

49

What value of x will make triangle cap o cap n cap m similar to triangle cap s cap r cap q by the SAS similarity theorem?

A

50

B

20

C

16

D

25

50

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 , 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.

B

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 .

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 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 .

51

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

line segment cap m cap n and line segment cap s cap r

D

angle cap s is congruent to angle cap n

52

Which mathematical statement is missing?

A

the fraction with numerator cap b cap c and denominator cap y cap z is equal to 6 thirds

B

angle cap b is congruent to angle cap y

C

angle cap b is congruent to angle cap z

D

the fraction with numerator cap y cap z and denominator cap b cap c is equal to 6 thirds

53

What value of x will make the triangles similar by the SSS similarity theorem?

A

30

B

67 point 5

C

1 point 5

D

20

54

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 g is congruent to angle i

D

angle cap e is congruent to angle cap h

55

What value of x will make the triangles similar by the SSS similarity theorem?

A

77

B

59

C

15 point 9

D

96 point 8

56

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

57

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 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.

B

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 .

C

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 .

D

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.

58

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

A

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 .

B

Show that the ratios the fraction with numerator cap x cap z and denominator cap w cap u and the fraction with numerator cap z cap y and denominator cap w cap v are equivalent, and angle cap u is congruent to angle cap z .

C

Show that the ratios the fraction with numerator cap u cap w and denominator cap z cap x and the fraction with numerator cap x cap y and denominator cap w cap v are equivalent, and angle cap w is congruent to angle cap x .

D

Show that the ratios the fraction with numerator cap x cap y and denominator cap v cap u and the fraction with numerator cap y cap z and denominator cap v cap w are equivalent, and angle cap u is congruent to angle cap x .

59

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 g is congruent to angle i

C

angle cap f is congruent to angle cap j

D

angle cap e is congruent to angle cap h

60

What value of x will make triangle cap o cap n cap m similar to triangle cap s cap r cap q by the SAS similarity theorem?

A

20

B

50

C

25

D

16

Triangle Similarity: SSS and SAS — Quiz Answers

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