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  • In triangles ABC and DEF, angle B = angle E, angle F = angle C and AB = 3 DE. Then, the two triangles are (A) congruent but not similar (B) similar but not congruent (C) neither congruent nor similar (D) congruent as well as similar

In triangles ABC \; \text {and} \; DEF, \angle B = \angle E, \angle F = \angle C \; \text {and}\; AB = 3 DE. Then, the two triangles are

(A) congruent but not similar  (B) similar but not congruent

(C) neither congruent nor similar      (D) congruent as well as similar  

Answers (1)

Answer : [B]

In \Delta ABC and \Delta DEF

\angle B=\angle E\; \text {and}\; \angle F=\angle C\; \text {also}\; AB=3DE

In \Delta ABC and \Delta DEF

\angle B=\angle E                      (given)

\angle F=\angle C                       (given)

\angle A=\angle D                       (third angle)

Therefore \Delta ABC\sim \Delta DEF              (by AAA similarity)

Also, it is given that AB=3DE

\Rightarrow AB\neq DE

Hence \Delta ABC and \Delta DEF is not congruent because congruent figures have the same shape and same size.

Therefore the two triangles are similar but not congruent.

Posted by

infoexpert23

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