In the given figure, AB || CD and O is the midpoint of AD.

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

 

Solution:

Given: In the given figure, AB || CD and O is the midpoint of AD.

To prove:
(i) ΔAOB ≅ ΔDOC.
(ii) O is the midpoint of BC.

Proof:
(i) In ΔAOB and ΔDOC,
BAO = ∠CDO                    (Alternate interior angles, AB || CD)
AO = DO                              (Given, O is the midpoint of AD)
AOB = ∠DOC                   (Vertically opposite angles)

∴ By ASA congruence criteria,
ΔAOB ≅ ΔDOC

(ii) ∵ ΔAOB ≅ ΔDOC           [From (i)]
∴ BO = CO                           (CPCT)
Hence, O is the midpoint of BC.

 

Leave a comment

Comments

Manish Kumar
June 30, 2024, 6:35 a.m.
Very very thank you
Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now