Question

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.

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

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB. Show that (i) ∠ DAC = ∠ BCA and (ii) ABCD is a parallelogram.