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

Apply trigonometry to general triangles.

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

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

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

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

Find arc lengths and areas of sectors of circles.

Prove geometric theorems.

Explain volume formulas and use them to solve problems.

Understand congruence in terms of rigid motions.

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

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

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

Prove theorems involving similarity.

Understand similarity in terms of similarity transformations.

Experiment with transformations in the plane.

Reason with shapes and their attributes.

Define trigonometric ratios and solve problems involving right triangles.

Make geometric constructions.

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

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

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

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

Understand and apply the Pythagorean Theorem.

Apply geometric concepts in modeling situations.
problem_activity: Task
Suppose $f$ is the map of the plane which takes each point $(x,y)$ to the point $(x-3,y)$ and $g$ is the map of the plane that takes each $(x,y)$ to $(3x,y)$.
Below is a triangle $ABC$.
[IMG]
Show the image of $\triangle ABC$ after applying each of the maps $f$ and $g$.
Does $f$ preserve distances and angles? Explain.
Does $g$ preserve distances and angles? Explain.


correct_option_index: 17