Question

Diagonal bd of a parallelogram abcd trisects at p and q.Prove that cq ||ap

Answer 1

When you draw the diagram, you may observe that we get two triangles APD and CQB which are congruent.

They are congruent by SAS congruence :-

1. AD = CB (Sides of parallelogram)
2. AP = CQ ( Trisected parts from question)
3. Angle ADP = Angle CBQ

By CPCT, angle APD = angle CQB

Now, if you extend the lines AP and CQ, we get to satisfy the condition that angle APD = angle CQB by vertically oppposite angles with DB being the transversal.

Therefore, we can conclude that AP ll CQ

Hence proved.

Hope this helps :)