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

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

Understand congruence in terms of rigid motions.

Prove theorems involving similarity.

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

Experiment with transformations in the plane.

Prove geometric theorems.

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

Define trigonometric ratios and solve problems involving right triangles.

Understand similarity in terms of similarity transformations.

Analyze, compare, create, and compose shapes.

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

Find arc lengths and areas of sectors of circles.

Understand and apply the Pythagorean Theorem.

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

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

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

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

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

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

Apply trigonometry to general triangles.

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

Use coordinates to prove simple geometric theorems algebraically.

Make geometric constructions.

Apply geometric concepts in modeling situations.

Understand and apply theorems about circles.
problem_activity: Task
Suppose $P$ is a point not contained on a line $L$.
Let $Q$ be the point on $L$ so that $PQ$ meets $L$ perpendicularly and let
$R$ be any other point on $L$ as in the picture below:
[IMG]
Show that segment $PQ$ is shorter than segment $PR$.


correct_option_index: 8