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Chapter 3: Q28 (page 98)

Given: GKbisects鈭�JGI

m鈭�H=m鈭�1

Prove: GK鈭�HI

Short Answer

Expert verified

It is proved that GK鈭�HI.

Step by step solution

01

Step 1. Apply exterior angle theorem.

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

m鈭�JGI=m鈭�H+m鈭�I=m鈭�I+m鈭�I=2m鈭�I

02

Step 2. Apply definition of angle bisector.

Here, GK炉bisects 鈭�JGI, therefore,

m鈭�KGI=12m鈭�JGI=12脳2m鈭�I=m鈭�I

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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