State the theorem regarding the exterior angle of a triangle.

In △ABC, the side BC is produced to D. If BA^C=60∘ and AB^C=50∘, find the magnitude of the exterior angle AC^D.

State the theorem regarding the sum of the interior angles of a triangle.

The interior angles of a triangle are in the ratio 2 : 3 : 4. Find the magnitude of each angle.

What is an isosceles triangle?

State the theorem regarding the angles opposite the equal sides of an isosceles triangle.

In △ABC, AB=AC and AB^C=50∘. Find the magnitude of BA^C.

State the converse of the theorem on isosceles triangles.

In △PQR, PQ^​R=QP^R. What can be concluded about the sides of the triangle?

In △ABC, AB^C=50∘ and BA^C=80∘. Identify the pair of equal sides, if any.

In △ABC, AB=AC. The side BA is produced to E. The angle EA^C is bisected by AD. Prove that AD is parallel to BC.

The diagonals of a parallelogram ABCD intersect at O. Prove that △AOB≡△COD.

In square ABCD, the points P and Q lie on sides AB and AD respectively such that PC^Q=45∘. Prove that BP=QD.

In △ABC, D is the midpoint of BC. If BD=DA, prove that BA^C is a right angle.

Prove that in an isosceles triangle, the perpendicular drawn from the apex to the opposite side bisects the apex angle.