Line segment AB is parallel to another line segment CD and O is the midpoint of AD.

State whether the statement regarding above information is true or false.

$ΔAOB ≅ ΔDOC$ .

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True

False

answer is A.

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Detailed Solution

Given, line segment AB is parallel to another line segment CD and O is the midpoint of AD.
Question Image

BC is the transversal.
In the figure, ∠ABO = ∠DCO [opposite angles].
Also, since lines AD & BC intersect, ∠AOB = ∠DOC.
Now, consider

△ AOB

and

△ DOC

.
∠AOB = ∠DOC (Opposite angles are equal)
∠ABO = ∠DCO (Alternate interior angles are equal)
OA = OD (Since O is the midpoint of AD)
Thus,

ΔAOB ⩭ ΔDOC

. [By ASA congruence rule].
So, the given statement is true and the correct option is 1.

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