Question

1. for △efg shown below, construct the angle bisectors of all three angles. if you do this carefully, all three angle bisectors will intersect at a common point (will be concurrent).

Explanation:

Step1: Recall the in - center property

The in - center of a triangle is the point of intersection of the angle bisectors of a triangle.

Step2: Use the property for \(\triangle EFG\)

For any triangle, the angle bisectors are concurrent. When constructing the angle bisectors of \(\angle E\), \(\angle F\), and \(\angle G\) of \(\triangle EFG\), they will intersect at the in - center of the triangle.

Answer:

The angle bisectors of \(\triangle EFG\) will intersect at the in - center of the triangle.