In `DeltaABC`, AD is the perpendicular bisector of BC (See adjacent figure). Show that` DeltaABC` is an isosceles triangle in which AB = AC.

DeltaABC is an isosceles triangle in which AB = AC. Show that /_ B = /_ C.

In DeltaABC , the bisector AD of /_BAC intersects BC at D . Prove that the DeltaABC is an isoceles triangle.

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

In the figure beside is a point on the extended part of CB . DeltaABC is an isosceles triangle of which AB=AC . IF AD bot BC and EF bot AC , then prove that DeltaABD~DeltaECF .

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

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)

In DeltaABC , the point at which the bisectors of the angles /_ABC and /_BAC intersect is called the incentre of the triangle.

In the given figure, AB||DC and AD||BC show that DeltaABC ~= Delta CDA .

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that (i) DeltaABD ~= DeltaACE (ii) AB = AC i.e., ABC is an isosceles triangle.

ABC is an isosceles triangle of which AC=BC and AB^(2) = 2AC^(2) . Then value of /_C will be -