LE 1 AD, BE and CF, the altitudes of Î ABC are equal, prove that Î

1.	LE 1 AD, BE and CF, the altitudes of Î ABC are equal, prove that Î ABC is anaquilateral triangle.
Answer» In triangle ABE and triangle ACF BE=CF (Given) ∠A=∠A (Common) ∠AEB=∠AFC=90° By AAS congruent rule ABE ≅ ACF AB=AC (CPCT) Similarly BCF ≅ ABD AB=BC AC=BC AB=AC AB = BC = AC..... Proved The triangle is a equaliteral triangle .

LE 1 AD, BE and CF, the altitudes of Î ABC are equal, prove that Î ABC is anaquilateral triangle.

Answer»

In triangle ABE and triangle ACF

BE=CF (Given)

∠A=∠A (Common)

∠AEB=∠AFC=90°

By AAS congruent rule ABE ≅ ACF

AB=AC (CPCT)

Similarly

BCF ≅ ABD

AB=BC

AC=BC

AB=AC

AB = BC = AC..... Proved

The triangle is a equaliteral triangle .