options: Prove theorems involving similarity.

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

Find arc lengths and areas of sectors of circles.

Use coordinates to prove simple geometric theorems algebraically.

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

Understand and apply theorems about circles.

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

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Explain volume formulas and use them to solve problems.

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

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

Analyze, compare, create, and compose shapes.

Prove geometric theorems.

Make geometric constructions.

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

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

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

Experiment with transformations in the plane.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

Apply geometric concepts in modeling situations.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Understand similarity in terms of similarity transformations.

Understand congruence and similarity using physical models, transparencies, or geometry software.
problem_activity: Task
Let $C$ be a circle with center $O$ and a diameter meeting $C$ in points
$P$ and $S$ as shown below:
[IMG]
With straightedge and compass, show how to find  a point $Q$ on $C$ so that triangle $OPQ$ is equilateral.
Repeating part (a) show how to find points $R, T, U$ on $C$ so that
$PQRSTU$ is a regular hexagon.
Find the area of $PQRSTU$.  How does it compare to the area of $C$?


correct_option_index: 14