Question

If ABC is an isosceles triangle with AB=AC. BD and CE are two medians of the triangle. Prove that BD=CE.

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.

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