BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

AD, BE and CF are altitudes of triangle ABC. If AD = BE = CF, prove that triangle ABC is an equilateral triangle.

If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

AX and DY are altitudes of two similar triangles Delta ABC and Delta DEF . Prove that AX : DY = AB : DE.

In a triangle ABC, sin A- cos B = Cos C , then angle B is

In triangle ABC, AD is the perpendicular bisector of BC (see the given figure). Show that triangle ABC is an isosceles triangle in which AB = AB .

ABC is an isosceles trian gle in w h ich altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

Prove that the triangle ABC is equilateral if cotA+cotB+cotC=sqrt3

In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that angle ABD = angle ACD .

In triangle ABC , the bisector AD of angle A is perpendicular to side BC (see the given figure). Show that AB = AC and triangle ABC is isosceles.