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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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Most popular questions from this chapter

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If two lines intersect to form right angles, then the lines are perpendicular.

State the postulate or theorem that justifies each statement.

鈭�3鈮�鈭�6

The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?

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Complete each statement with the word always, sometimes, or never.

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