In the following figure, AB = EF, BC = DE and ∠B = ∠E = 90°. Prove that AD = FC.

A point O is taken inside a rhombus ABCD such that its distances from the vertices B and D are equal. Show that AOC is a straight line.

In the given figure, ABCD is a rectangle and X and Y are the mid-points of the sides DC and AB respectively. P and Q are the points of AD and BC respectively such that DP = BQ.

Prove that △ APX ≅ △ CQY.

Mrs. Sharmila, a mathematics teacher of class 9 started a very important geometry chapter on Congruency in triangles and decided to test the previous concept by setting a geometry problem on the blackboard. In △ ABC, AD is drawn as perpendicular bisector of BC. It is given that AD = 9 cm and BC = 24 cm.

Based on the above information answer the following:

(i) Prove △ ABD ≅ △ ACD

(ii) Assign a special name to △ ABC

(iii) Calculate perimeter of △ABC.

(iv) Calculate Area of △ABC.