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.

$ΔAOB ≅ ΔDOC$ .

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE