standard_description: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
problem_activity: Task
The goal of this task is to explain why the area enclosed by a circle $C$ of radius $r$ is
$\pi r^2$.  Recall that $\pi$ is the ratio of the circumference of a circle to its diameter and that this ratio is independent of the size of the circle.
Draw a picture of a regular octagon $O$ inscribed in $C$.  Find  a formula for the area of the octagon in terms of its perimeter.
Reasoning as in part (a), find a formula for the area of a regular $n$ sided polygon, for $n \geq 3$, inscribed in $C$: the formula should give the area of the polygon  in terms of  its perimeter.
Using your formula from part (b), explain why the area of $C$ is $\pi r^2$.


aligns: no