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

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

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.

Prove geometric theorems.

Experiment with transformations in the plane.

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

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

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

Explain volume formulas and use them to solve problems.

Analyze, compare, create, and compose shapes.

Apply geometric concepts in modeling situations.

Make geometric constructions.

Apply trigonometry to general triangles.

Use coordinates to prove simple geometric theorems algebraically.

Find arc lengths and areas of sectors of circles.

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

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

Prove theorems involving similarity.

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

Understand and apply the Pythagorean Theorem.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
problem_activity: Task
Pablo is practicing bank shots on a standard 4 ft.-by-8 ft. pool table that has a wall on each side, a pocket in each corner, and a pocket at the midpoint of each eight-foot side.
Pablo places the cue ball one foot away from the south wall of the table and one foot away from the west wall, as shown in the diagram below.  He wants to bank the cue ball off of the east wall and into the pocket at the midpoint of the north wall.
[IMG]
At what point should the cue ball hit the east wall?
After Pablo practices banking the cue ball off of the east wall, he tries placing the eight-ball two feet from the east wall, as shown in the diagram below, so that if he shoots the cue ball exactly as he did before, the cue ball will strike the eight-ball directly and sink the eight-ball into the north pocket.  How far from the north wall should Pablo place the eight-ball?
[IMG]


correct_option_index: 23