options: Apply geometric concepts in modeling situations.

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

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

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

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

Prove geometric theorems.

Prove theorems involving similarity.

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

Understand and apply theorems about circles.

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

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

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

Use coordinates to prove simple geometric theorems algebraically.

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

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Reason with shapes and their attributes.

Analyze, compare, create, and compose shapes.

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

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

Understand similarity in terms of similarity transformations.

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

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

Understand congruence in terms of rigid motions.

Define trigonometric ratios and solve problems involving right triangles.
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: 7