Question

based on the given diagram, complete the sentence below.
answer
point ( d ) is the of ( \triangle a b c ) because ( overline{d e}, overline{d f} ), and ( overline{d g} ) are all

Explanation:

Step1: Recall the definition of the in - center

The in - center of a triangle is the point where the angle bisectors of the triangle intersect. Also, the in - center is equidistant from all the sides of the triangle.

Step2: Analyze the given diagram

In the diagram, \(DE\perp AB\), \(DF\perp BC\), and \(DG\perp AC\). Since \(DE\), \(DF\), and \(DG\) are the perpendicular distances from point \(D\) to the sides \(AB\), \(BC\), and \(AC\) of \(\triangle ABC\) respectively.

Answer:

Point \(D\) is the in - center of \(\triangle ABC\) because \(\overline{DE}\), \(\overline{DF}\), and \(\overline{DG}\) are all the perpendicular distances from \(D\) to the sides of the triangle.