Question

Given that E is the midpoint of ¯¯¯¯¯¯AD and ¯¯¯¯¯¯ BC, which of the following proves that ¯¯¯¯¯¯AB∥¯¯¯¯¯¯CD?

Answer 1

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.

Step-by-step explanation:

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