options: Make geometric constructions.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Apply geometric concepts in modeling situations.

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

Understand similarity in terms of similarity transformations.

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

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

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

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

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

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

Understand and apply theorems about circles.

Understand congruence in terms of rigid motions.

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

Apply trigonometry to general triangles.

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

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

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

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

Prove geometric theorems.
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