Answer:
see attached for a graph
a. BA≅BC (the compass told me so)
c. AD≅CD
Explanation:
You want a graph of ∆ABC, with A(4, 7), B(0, 0), and C(8, 1). You want to identify the congruent sides, construct an angle bisector, and comment on how it divides the opposite side.
Graph
The graph of the points, and the construction of the angle bisector are shown in the attachment.
a. Congruent sides
Since you have your compass available for construction, you can use set it to the measure of one side and compare that to the other two sides. It does not take long to identify AB ≅ BC. (A compass setting shows they are the same length.)
b. Angle bisector
As you know, an angle bisector is constructed by first identifying two points on the sides of the angle that are the same distance from the vertex of the angle. Then two intersecting arcs are drawn with the same radius using those points as their centers. The vertex and the intersection of the arcs defines the ray that is the angle bisector. This is shown in the attachment.
c. AD and CD
You can count grid squares (or use the compass) to determine that AD and CD are the same length: D is the midpoint of AC.
This reinforces your knowledge that the angle bisector of the a.pex angle of an isosceles triangle is also an altitude and a median.