options: Prove geometric theorems.

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

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.

Explain volume formulas and use them to solve problems.

Understand similarity in terms of similarity transformations.

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

Find arc lengths and areas of sectors of circles.

Understand and apply theorems about circles.

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

Apply geometric concepts in modeling situations.

Make geometric constructions.

Experiment with transformations in the plane.

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

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

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply the Pythagorean Theorem.

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

Analyze, compare, create, and compose shapes.

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

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

Reason with shapes and their attributes.

Apply trigonometry to general triangles.

Define trigonometric ratios and solve problems involving right triangles.

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

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.
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