In the given figure, AB || CD and O is the midpoint of AD. Show that(i

1.	In the given figure, AB \|\| CD and O is the midpoint of AD. Show that(i) △ AOB ≅ △ DOC(ii) O is the midpoint of BC.
Answer» (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 (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.

In the given figure, AB || CD and O is the midpoint of AD. Show that(i) △ AOB ≅ △ DOC(ii) O is the midpoint of BC.

Answer»

(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

(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.