Question

In the given figure, AB || CD and O is the midpoint of AD.
Show that
(i) ΔAOB ≅ ΔDOC.
(ii) O is the midpoint of BC.​

Answer 1

(i) IN TRIANGLE AOB AND TRIANGLE DOC

angle B= angle C

angle AOB= angle cod

AO=OD

THEREFORE BY AAS CONGRUENCE RULE BOTH THE TRIANGLE ARE CONGRUENT

(ii) by cpct OB = OC

Step-by-step explanation:

HOPE IT HELPS

FOLLOW ME AND THANKS

Answer 2

Given :-

∠ BAO = ∠ CDO

AO = DO

To Find :-

Show that  △ AOB ≅ △ DOC

Show that O is the midpoint of BC.

Solution :-

Solution I :

From the figure △ AOB and △ DOC

We know that AB || CD and ∠ BAO and ∠ CDO are alternate angles

So we get,

∠ BAO = ∠ CDO

From the figure we also know that O is the midpoint of the line AD

We can write it as AO = DO

According to the figure, we know that

∠ AOB and ∠ DOC are vertically opposite angles.

So we get, ∠ AOB = ∠ DOC

Therefore, by ASA congruence criterion we get

△ AOB ≅ △ DOC

Solution II :

We know that, △ AOB ≅ △ DOC

So we can write it as

BO = CO (c. p. c. t)

Therefore, it is proved that O is the midpoint of BC.