options: Make geometric constructions.

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

Understand and apply the Pythagorean Theorem.

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

Experiment with transformations in the plane.

Explain volume formulas and use them to solve problems.

Understand and apply theorems about circles.

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

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Find arc lengths and areas of sectors of circles.

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

Understand similarity in terms of similarity transformations.

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

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

Prove theorems involving similarity.

Apply geometric concepts in modeling situations.

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

Prove geometric theorems.

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

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

Reason with shapes and their attributes.

Define trigonometric ratios and solve problems involving right triangles.

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

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
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: 0