Question

AM, BN, CQ are the altitudes of triangle ABC and are equal. Prove that triangle ABCD is an equilateral triangle.

Answer 1

Here is your solution

Answer 2

GIVEN :

AM, BN, CQ are the altitudes of triangle ABC and are equal.

TO FIND :

Prove that triangle ABCD is an equilateral triangle.

SOLUTION :

◆Draw ∆ABC , with attitude QC,BN,AM.

◆Consider ∆ABN , ∆ACQ.

◆<A is common in between.

◆<ANB, <AQC are 90° , since ◆altitudes cuts at 90° of a triangle .

QC =BN (Given )

◆Thus,

∆ABN = ∆ACQ. Both are congruent.

◆AB = AC .

◆Similarily we can prove,

BC =AC .

◆By proving ∆BCN, ∆AMC are congruent.

◆Since , AB=AC=BC .

∆ABC is an equilateral triangle.