options: Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

Visualize relationships between two-dimensional and three-dimensional objects.

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Prove theorems involving similarity.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Understand similarity in terms of similarity transformations.

Solve real-world and mathematical problems involving area, surface area, and volume.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Understand congruence in terms of rigid motions.

Classify two-dimensional figures into categories based on their properties.

Experiment with transformations in the plane.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Translate between the geometric description and the equation for a conic section.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Make geometric constructions.

Reason with shapes and their attributes.

Analyze, compare, create, and compose shapes.

Prove geometric theorems.
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 $\pi r^2$.


correct_option_index: 18