1.

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»

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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