standard_description: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
problem_activity: Task
Suppose $\overline{AB}$ is a diameter of a circle and $C$ is a point on the circle different from $A$ and $B$ as in the picture below:
[IMG]
Show that triangles $COB$ and $COA$ are both isosceles triangles.
Use part (a) and the fact that the sum of the angles in triangle $ABC$ is $180$ degrees to show that angle $C$ is a right angle.


aligns: no