8.
A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. So:
[tex]\begin{gathered} AM\cong MB \\ MC\cong CM_{\text{ }}Reflexive_{\text{ }}property \\ m\angle AMC\cong m\angle BMC_{\text{ }}Perpendicular_{\text{ }}bisector \end{gathered}[/tex]
Therefore:
[tex]\Delta AMC\cong\Delta BMC_{\text{ }}SAS_{\text{ }}Theorem[/tex][tex]m\angle CAM\cong\angle CBM_{\text{ }}CPCTC[/tex]
We can conclude that:
[tex]\Delta ABC[/tex]
Is an isosceles triangle
