Q2 plz experts give solution

Q2 plz experts give solution 1. In triangle ABC, M is mid-point of AB and a straight line through M and parallel to BC cuts AC at N. Find the lengths of AN and MN, if BC = 7 cm and AC = 5 cm. 2. Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus. 3. D, E and F are the mid-points of the sides AB, BC and CA of an isosceles A ABC ir which AB = BC. Prove that A DEF is als( isosceles. 4. The following figure shows a trapeziun ABCD in which AB // DC. P is the mid-poir of AD and PR // AB. Prove that : 1 PR = — (AB + CD) 2 D c

Dear student

Here is the proof for the mentioned result:

Let ABCD is a rectangle such as AB = CD and BC = DA. P, Q, R and S are the mid points of the sides AB, BC, CD and DA respectively.

However, the diagonals of a rectangle are equal.

∴ AC = BD … (5)

By using equation (1), (2), (3), (4), and (5), we obtain

PQ = QR = SR = PS

Therefore, PQRS is a rhombus.

Hope! This will help you!

Regards