91Ó°ÊÓ

Parallel lines are the lines in a plane that do not intersect each other at any point.

Transversal is a line that intersect two or more lines in a plane.

Draw required figure with appropriate instructions.

A figure shows, two parallel lines, $\stackrel{¯}{AB},\stackrel{¯}{CD}$ and a transversal, $\stackrel{¯}{EF}$.

When two parallel lines are intersected by a transversal, the angles formed on the same side of the transversal and on the interior of the two lines are called same side interior angles.

Draw required figure with appropriate instructions.

The bisectors,$\stackrel{¯}{GI}$ and$\stackrel{¯}{HI}$ are drawn using protractor.

An angle bisector divides an angle into two equal parts.

Draw required figure with appropriate instructions.

$∠GIH$is formed by bisectors, $\stackrel{¯}{GI}$and $\stackrel{¯}{HI}$. We have noticed that the measure of$∠GIH$ is $90°$.

If two parallel lines are intersected by a transversal, then the same side interior angles are supplementary.

From the figure it can be observed that,$∠BHG$ and$∠HGD$ are same side interior angles then by property of parallel lines,

$$\begin{gathered} m∠BHG+m∠HGD=180 \\ m∠3+m∠4+m∠1+m∠2=180 \\ 2m∠3+2m∠2=180 \\ m∠3+m∠2=90 \end{gathered}$$

Consider$∠GIH$, then by an angle sum theorem,

$$\begin{gathered} m∠2+m∠3+m∠5=180 \\ 90+m∠5=180 \\ m∠5=180−90 \\ =90 \end{gathered}$$

Therefore, the measure of$∠GIH$ is $90°$.