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

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

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

Analyze, compare, create, and compose shapes.

Prove geometric theorems.

Make geometric constructions.

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

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

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

Find arc lengths and areas of sectors of circles.

Understand and apply theorems about circles.

Apply trigonometry to general triangles.

Reason with shapes and their attributes.

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

Understand congruence in terms of rigid motions.

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

Understand and apply the Pythagorean Theorem.

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

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

Apply geometric concepts in modeling situations.

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

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.

Define trigonometric ratios and solve problems involving right triangles.

Draw, construct, and describe geometrical figures and describe the relationships between them.
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: 8