Question

Given: Line Segment AB is perpendicular to Line Segment BC, Line Segment DC is perpendicular to Line Segment BC, Line Segment AC is congruent to Line Segment DB

Prove: Line Segment AE is congruent to Line Segment DE

Write a two-column proof for this.

Answer 1

Answer:

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

Then, O is the midpoint of BC.

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