Question

in the given figure ab parallel to CD and O is the midpoint of ad show that triangle aob congruent to triangle Doc and o is the midpoint of BC

Answer 1

Answer:

Step-by-step explanation:

Given: AB ║ CD and O is the midpoint of AD.

To prove: triangle AOB congruent to triangle DOC and O is the midpoint of BC

Proof:

=> In ΔAOB and ΔDOC, alternate interior angles, AB ║CD

So, ∠BAO = ∠CDO

As, O is the midpoint of AD,

∴ AO = DO

∠AOB = ∠DOC [vertically opposite angles]

Thus, According to ASA congruence criteria,

Δ AOB ≅ Δ DOC

Hence, triangle AOB congruent to triangle DOC.

=> As, triangle AOB congruent to triangle DOC,

BO = CO (Corresponding parts of Congruent Triangles)

Therefore, O is midpoint of BC.

Answer 2

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