Question

1. if g is the mid - point of ab, classify each triangle by its angles and sides. * 5 points

triangle bec:
acute, scalene
right, scalene
acute, isosceles
equilateral, equiangular

Explanation:

Step1: Check angles

Since there is a right - angle symbol at $\angle BFC = 90^{\circ}$, but we are looking at $\triangle BEC$. In $\triangle BEC$, all angles are less than $90^{\circ}$, so it is an acute triangle.

Step2: Check side - lengths

The side - lengths of $\triangle BEC$ are $BE = 6$, $EC = 5$, and $BC$ can be found using the Pythagorean theorem in right - triangle $BFC$ where $BF = 8$ and $FC$ is part of the right - triangle setup. But just from the given side - lengths $BE = 6$ and $EC = 5$, we can see that $BE
eq EC$. However, if we consider the right - triangle relationships and the given information more closely, we find that $BE = 6$ and $BC=\sqrt{8^{2}+FC^{2}}$ and $EC = 5$. By observing the figure and using basic geometric knowledge, we can note that two sides of $\triangle BEC$ are equal. So it is an isosceles triangle.

Answer:

acute, isosceles