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

Make geometric constructions.

Understand and apply theorems about circles.

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

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

Prove theorems involving similarity.

Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Prove geometric theorems.

Apply geometric concepts in modeling situations.

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

Apply trigonometry to general triangles.

Analyze, compare, create, and compose shapes.

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

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

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

Understand and apply the Pythagorean Theorem.

Experiment with transformations in the plane.

Use coordinates to prove simple geometric theorems algebraically.

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

Understand congruence in terms of rigid motions.

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.

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

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.
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: 1