Which diagram can be used to prove △abc ~ △dec using similarity transformations?

Asked by wiki @ in Mathematics viewed by 637 People

Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?
(from top to bottom, first pictures top option is A for example)

A.
B.
C.
D.

Answered by wiki @

Answer:

Step-by-step explanation:

(A) From the given figure, ∠BAC=∠CDE and ∠ACB=∠DCE=90°.

Thus, from ΔABC and ΔDEF, we have

∠BAC=∠CDE (Given)

∠ACB=∠DCE=90°

Thus, by AA similarity rule,

ΔABC is similar to ΔDEF.

Therefore, this option is correct.

(B) From the given figure, ∠ABC=∠DCE and ∠ACB=∠DEC

But, there is no angle and side is similar to the other angle or side of the triangle. Thus, this option is not correct.

(C) From the given figure, ∠ABC=∠ACB and ∠DCE=∠DEC

But, there is no angle or side is similar to the other angle or side of the triangle. Thus, this option is not correct.

(D) From the given figure, ∠BAC=∠CDE

But, there is no another angle or side is similar to the other angle or side of the triangle. Thus, this option is not correct.

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