We only need to check if the corresponding angles are equal for two triangles to be similar.
A
True
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B
False
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Solution
The correct option is A True Take two triangles ABC and DEF such that ∠A=∠D,∠B=∠Eand∠C=∠F Cut DP = AB and DQ = AC and join PQ. So, ΔABC≅ΔDPQ (SAS congruence) This gives ∠B=∠P=∠E and PQ || EF. Therefore, DPPE=DQQF⇒PEDP=QFDQ⇒PEDP+1=QFDQ+1⇒DP+PEDP=DQ+QFDQ⇒DEDP=DFDQ DP = AB and DQ = AC, ⇒DEAB=DFAC ABDE=ACDF Similarly, ABDE=BCEF and so ABDE=BCEF=ACDF Hence, if corresponding angles are equal in two triangles, they are similar as the ratio of corresponding sides is the same.