Question

In the figure, O is the mid-point of AB and CD, prove that AC = BD

Answer 1

Proved: AC = BD

Explanation:

The complete question related to this with diagram can be found at toppr website.

Given: O is the mid point of AB and CD

Find attached the diagram

∠COA = ∠BOD (vertical angles are equal)

∠AOD = ∠COB (vertical angles are equal)

For ∆AOC

AC + OC + OA = 180° (sum of angles in a triangle)

For ∆DOB

DB + OB + OD = 180° (sum of angles in a triangle)

OC = OD (sides are equal)

OA = OB (sides are equal)

Since both ∆AOC and ∆DOB are equal to 180°, AC = DB.

DB = BD

Proved: AC = BD