Question

1. How the angle bisector of a parallelogram form a rectangle?

2. If an angle of parallelogram is two-third of its adjacent angle. find the angles of the parallelogram?

3. Find the measures of all the angles of a parallelogram is one angle is 24 degree less than twice the smallest angle?

4. AB and CD are two parallel lines and a perpendicular angle intersect AB at X and CD at Y. Prove that the bisector of the interior angle form a rectangle?

5. ABCD is a parallelogram and line segment AX bisects the angle A and C respectively, show that AX II CY.

6. Given ABC, lines are drawn through A, B, and C respectively parallel to the side BC, CA and AB forming triangle PQR. Show that BC = 1/2 QR.

7. BM and CN are perpendicular to a line passing through the vertex A of a triangle ABC, if the angle is the midpoint of BC. Prove that angle M = angle N.

Answer 1

I have answered only first question as it was difficult to type answers of all the questions.
I would request other people who want to answer these questions to please answer rest of the questions except the first one.