Question

In the diagram, StartFraction S Q Over O M EndFraction = StartFraction S R Over O N EndFraction = 4.

Triangles M N O and S R Q are shown. The length of side N O is 8 and the length of side R Q is 48. The length of side O M is 15 and the length of Q S is 60. The length of side M N is 12 and the length of S R is 32.To prove that the triangles are similar by the SSS similarity theorem, which other sides or angles should be used?

MN and SR
MN and QR
∠S ≅ ∠N
∠S ≅ ∠O

Answer 1

Given :  SQ/OM =  SR/ON = 4

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

MN and SR

MN and QR

∠S ≅ ∠N

∠S ≅ ∠O

Solution:

SSS ( Side Side Side)

Similarity all corresponding sides have same proportion

SQ/OM =  SR/ON = 4  already given

Missing Ration is   QR  and MN

QR/MN should be 4 for similar triangles

SQ/OM =  SR/ON =  QR/MN     (similar triangle)

Hence MN and QR  should use used

SQ/OM = 60/15 = 4

SR/ON = 32/8 = 4

QR/MN = 48/12  = 4

MN and QR sides be used

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