Thread: Prove that two lines are parallel in a given geometry

1. Prove that two lines are parallel in a given geometry

Attached are the question and solution for part (a) and (b).

For part (c), how to prove that EF is parallel to AC?

Thank you.

2. Re: Prove that two lines are parallel in a given geometry

Hi Yeoky,
Complete the following constructions to your drawing

Extend BH to AD @ J BG to DC @K
connect JK,JE,KF,JE, EK

There are congruencies leading to BG= HD BH= GD BHDG is a parallelogram
Also EJ =FK EF=JK EJKF is a parallelogram
The perpendicular distance from AC to EF and JK are equal
EF is parallel to AC.

Find the congruent parts

3. Re: Prove that two lines are parallel in a given geometry

Its very simple just prove that figure a parallelogram by joining its all sides and diagonals.This will prove that the difference of two lines is equal at every point.
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