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

Prove theorems involving similarity.

Define trigonometric ratios and solve problems involving right triangles.

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

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

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

Understand congruence in terms of rigid motions.

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

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

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

Explain volume formulas and use them to solve problems.

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

Understand and apply the Pythagorean Theorem.

Find arc lengths and areas of sectors of circles.

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

Make geometric constructions.

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

Prove geometric theorems.

Apply trigonometry to general triangles.

Analyze, compare, create, and compose shapes.

Understand similarity in terms of similarity transformations.

Reason with shapes and their attributes.

Experiment with transformations in the plane.

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

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

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Task
Suppose $\overline{AB}$ is a diameter of a circle and $C$ is a point on the circle different from $A$ and $B$ as in the picture below:
[IMG]
Show that triangles $COB$ and $COA$ are both isosceles triangles.
Use part (a) and the fact that the sum of the angles in triangle $ABC$ is $180$ degrees to show that angle $C$ is a right angle.


correct_option_index: 8