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

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

Apply geometric concepts in modeling situations.

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

Find arc lengths and areas of sectors of circles.

Explain volume formulas and use them to solve problems.

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

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

Reason with shapes and their attributes.

Prove theorems involving similarity.

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

Understand and apply the Pythagorean Theorem.

Understand and apply theorems about circles.

Prove geometric theorems.

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

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

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

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

Analyze, compare, create, and compose shapes.

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

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.

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

Apply trigonometry to general triangles.
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: 6