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Question

In the given figures which of the triangles are similar?



A

ΔDEFΔSQR

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B

ΔFEDΔPQS

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C

ΔEDFΔQPS

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D

None of the triangles are similar

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Solution

The correct option is D

ΔEDFΔQPS


Two triangles are similar if the corresponding angles are equal and the ratio of corresponding sides is same.
So, we need to check which of the angles are equal in the available triangles.
EDF=SPQ=25
In ΔQPS,QSP=30 and SPQ=25
Since, sum of the angles in a triangle is 180,
PQS=1803025=125
Therefore, DEF=PQS=125.
Hence, by AA similarity, ΔEDFΔQPS


Mathematics

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