Question

Given: $\overline{GK}$bisects$\angle JGI$

$m\angle H=m\angle 1$

Prove: $\overline{GK}\parallel \overline{HI}$

Short answer

It is proved that $\overline{GK}\parallel \overline{HI}$.

Step-by-step solution

Step 1. Apply exterior angle theorem.

From the given diagram it can be observed that $\angle JGI$is exterior angle and are remote interior angles, such that,

$$\begin{gathered} m\angle JGI=m\angle H+m\angle I \\ =m\angle I+m\angle I \\ =2m\angle I \end{gathered}$$

Step 2. Apply definition of angle bisector.

Here, $\overline{GK}$bisects $\angle JGI$, therefore,

$\begin{array}{c}m\angle KGI=\frac{1}{2}m\angle JGI\\ =\frac{1}{2}\times 2m\angle I\\ =m\angle I\end{array}$

Which implies that the alternative angles are equal.

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, .