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Given: GKbisectsJGI

mH=m1

Prove: GKHI

Short Answer

Expert verified

It is proved that GKHI.

Step by step solution

01

Step 1. Apply exterior angle theorem.

From the given diagram it can be observed that JGIis exterior angle and are remote interior angles, such that,

mJGI=mH+mI=mI+mI=2mI

02

Step 2. Apply definition of angle bisector.

Here, GK¯bisects JGI, therefore,

mKGI=12mJGI=12×2mI=mI

Which implies that the alternative angles are equal.

03

Step 3. Description of step.

If the two lines are intersected by a transversal and alternative angle are equal then the two lines are parallel. Therefore, .

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