Question

line segment ab is parallel to another line segment cd. O is the midpoint ad. show that o is the mid point of bc

Answer 1

Step-by-step explanation:

Given: AB = CD ; O is the mid - point .

To proof : ABC is congruent to DOC

Proof : IN triangle AOB and DOC ,

AB = CD ( given )

<OAB = <ODC ( alternate interior angles )

<AOB = <DOC ( vertically opposite angles )

Therefore , triangle AOB is congruent to DOC (ASA rule )

OB = OC ( C.PC.CT)

Hence , O is also the mid point of BC

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Answer 2

Answer:

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Given: AB is parallel to another line segment CD.

O is the midpoint OF AD.

In ΔAOB and ΔDOC

∠AOB=∠COD.......(Vertically opposite angle )

∠BAO=∠CDO......(Given AB parallel to DC and AD meet both lines so alternate angles are equal)

AO=OD.........(O is the midpoint of AD )

ΔAOB≅ΔDOC........ASA test

So, BO=CO(by cpct)

Then, O is the midpoint of BC.

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