Question

In the adjoining figure, AC = BD. AE - FB and ACF - BDE 90° Prove that CF =DE AC equal DB​

Answer 1

Answer:

ANSWER:

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.

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