options: Experiment with transformations in the plane.

Explain volume formulas and use them to solve problems.

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

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

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

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

Understand similarity in terms of similarity transformations.

Prove geometric theorems.

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

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

Understand and apply theorems about circles.

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

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

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

Apply geometric concepts in modeling situations.

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

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.

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

Reason with shapes and their attributes.

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

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
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: 7