Question

In figure line segments ab is parallel to another line segments cd . O is the mid point of ad . So prove that triangle AOB is congruence to triangle DOC​

Answer 1

SOLUTION

Given, AB||CD. O is the mid point of AD.

To prove: Triangle AOB is congruent to triangle DOC

Proof: In triangles AOB and DOC

<OAB = <ODC [ alternate interior angles ]

AB = CD [ Since, AB//CD ]

<AOB = <DOC [ vertically opposite angel Therefore, Triangle AOB congruent to triangle DOC (by A.S.A criteria)

Now, OB= OC (By C.P.C.T)

Therefore, O is the mid point of BC.