Question

ABC is an isosceles triangle in which altitudes BD and CE are drawn to equal sides AC and AB respectively (see figure) Show that these altitudes are equal.

Answer 1

Here we use ASA congruenceASA(angle side angle):Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the  other triangle.

Given:

ΔABC is an isosceles∆ with AB = AC, BD and CE are altitudes.

To prove:

BD = CE

Proof:

In ΔAEC and ΔADB

∠A = ∠A. (Common)

∠AEC = ∠ADB (each 90°)

AB = AC (Given)

Therefore, ΔAEC ≅ ΔADB[by AAS congruence rule]

Thus, BD = CE (by CPCT)

Hence , altitudes BD & CE are equal.

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Answer 2

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