Prove that the bisectors of the opposite angles of a parallelogram are parallel.

Assuming the validity of the statement that the internal bisectors of the angles of a triangle are concurrent, prove that the altitudes of a triangle are concurrent.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.. (Recall that you have proved it in class IX).

The measures of two adjacent angles of a parallelogram are in the ratio 3:2 . Find the measure of each of the angles of the parallelogram.

Prove that the sum of the measures of four angles of a quadrilateral is 360^@ .

Prove that in two equiangular triangles the ratio of the corresponding sides and the ratio of the bisectors of the corresponding angles are equal. [The end-points of the bisectors are on the opposite sides of the angles.]

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Explain how a square is. a parallelogram

State whether True or False. All rhombuses are parallelograms