In `DeltaABC`, the bisector AD of A is perpendicular to side BC Show that AB = AC and `DeltaABC` is isosceles.

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.

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 .

In the given figure, DeltaABC is a right angled Deltawith /_B= 90^(@) and BD is perpendicular to AC. Prove that DeltaADB ~ DeltaABC

AD and BC are equal and perpendiculars to a line segment AB. Show that CD bisects AB.

angleACD is an exterior angle of DeltaABC and he bisector of angleA intersects BC at E. Prove that, angleABC+angleACD=2angleAEC .

Fill in the blanks so as to make each of the following statements true : In DeltaABC , AD is the bisector of /_A and D lies on BC. If AB= 6 cm, AC= 5 cm and BD= 3 cm, then BC="……….."cm .

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

D is midpoint of BC in Delta ABC such that AD and AC are perpendicular, Show that Cos A Cos C = (2 (c^2-a^2))/(3ac)

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

In the given figure, the line segment XY is parallel to side AC of DeltaABC and it divides the Deltainto two parts of equal areas. Find the ratio (AX)/(AB) .