Question

BD and CE are altitudes of ∆ABC such that BD = CE. Prove that CD = BE.

Answer 1

10th

Maths

Triangles

Criteria for Triangle Similarity

In a ABC BD and CE are the...

MATHS

In a △ABC BD and CE are the altitudes. Prove that △ADB and △AEC are similar. Check whether  △CDB  and △BEC are similar.



MEDIUM

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ANSWER

In △ABD and △AEC, we have

    ∠ADB=∠AEC               [Each equal to 90∘]

     ∠BAD=∠EAC                [Common]

So, by AA-criterion of similarity, we have

   △BDA∼△CEA   or,   △ADB∼△AEC.

Clearly, △CDB is not similar to △BEC, because they are not equiangular.