options: Understand and apply theorems about circles.

Prove geometric theorems.

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).

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

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

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

Apply trigonometry to general triangles.

Experiment with transformations in the plane.

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

Reason with shapes and their attributes.

Understand similarity in terms of similarity transformations.

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

Understand and apply the Pythagorean Theorem.

Define trigonometric ratios and solve problems involving right triangles.

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

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

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

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

Analyze, compare, create, and compose shapes.

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

Make geometric constructions.

Find arc lengths and areas of sectors of circles.

Draw, construct, and describe geometrical figures and describe the relationships between them.
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: 16