options: Explain volume formulas and use them to solve problems.

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

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

Prove geometric theorems.

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

Reason with shapes and their attributes.

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

Understand and apply the Pythagorean Theorem.

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

Understand similarity in terms of similarity transformations.

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

Experiment with transformations in the plane.

Analyze, compare, create, and compose shapes.

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

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

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

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

Make geometric constructions.

Solve real-world and mathematical problems involving area, surface area, and volume.
problem_activity: Task
Imagine you are a ninja that can slice solid objects straight through. You have a solid cube in front of you. You are curious about what 2-dimensional shapes are formed when you slice the cube. For example, if you make a slice through the center of the cube that is parallel to one of the faces, the cross section is a square:
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For each of the following slices, (i) describe using precise mathematical language the shape of the cross section. (ii) draw a diagram showing the cross section of the cube.
[IMG]
a. A slice containing edge AC and edge EG b. A slice containing the vertices C, B, and G. C. A slice containing the vertex A, the midpoint of edge EG, and the midpoint of edge FG.


correct_option_index: 24