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

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

Analyze, compare, create, and compose shapes.

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

Find arc lengths and areas of sectors of circles.

Make geometric constructions.

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

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

Understand and apply theorems about circles.

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

Reason with shapes and their attributes.

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

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

Prove theorems involving similarity.

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

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

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

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

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Experiment with transformations in the plane.

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

Define trigonometric ratios and solve problems involving right triangles.

Explain volume formulas and use them to solve problems.

Understand and apply the Pythagorean Theorem.
problem_activity: Task
Suppose we are given a circle of radius $r$.  The goal of this task is to construct an equilateral triangle whose three vertices lie on the circle.
Suppose $\overline{AB}$ is a diameter of the circle.  Draw a circle with center $A$ and radius $r$ and label the two points of intersection of the circles $P$ and $Q$ as pictured below:
[IMG]
Show that $m(\angle ABP) = 30$ and $m(\angle ABQ) = 30$.
Show that
$\triangle PBQ$ is an equilateral triangle inscribed in the given circle.


correct_option_index: 5