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
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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.

AD and BC are equal perpendiculars to a line segment AB (see the given figure) Show that CD bisects AB.

In quadrilateral ACBD. AC = AD and AB bisects angle A (see the given figure). Show that triangle ABC = triangle ABD . What can you say about BC and BD?

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

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that ( i ) triangle ABE ~= triangle ACF (ii) AB = AC i.e ABC is an isoceles triangle

triangle ABC is an isosceles tr ia n g le in w h ich AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that angle BCD is a right angle.

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

D is a point on side BC of triangle ABC such that AD = AC (see the given figure). Show that AB gt AD.

In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt AD.