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Question

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that AB = AC i.e. ABC is an isosceles triangle
569820_37529ef889234646b7cc3879a2d1a2b6.png

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Solution

Given ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal

In ΔADB and ΔACE

ADB=AEC=900 (altitudes BD and CE to sides AC and AB)

BD=CE (Given altitudes are equal)

BAD=CAE (Common angle )

ΔABDΔACE [by AAS congruence]

So AB=AC (by CPCT)

triangle ABC is an isosceles triangle

714311_569820_ans_e0bb695a6f044a3aadd884d73b445367.png

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