Question

Assertion (A): In △ABC, E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ = QP. Reason (R): Q is the midpoint of AP.

ABCD is a rhombus and P,Q,R,S are mid-points of AB, BC,CD and DA respectively. Prove that quadrilateral PQRS is a rectangle.

In a forest, a big tree got broken due to heavy rain and wind, Due to this rain the big branches AB and AC with lengths 5 m fell down on the ground. Branch AC makes an angle of 30° with the main tree AP. The distance of Point B from P is 4 m. You can observe that △ABP is congruent to △ACP.

In the middle of the city, there was a park ABCD in the form of a parallelogram form so that AB = CD, AB||CD and AD = BC, AD||BC. Municipality converted this park into a rectangular form by adding land in the form of △APD and △BCQ. Both the triangular shape of land were covered by planting flower plants.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if