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

Understand similarity in terms of similarity transformations.

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

Explain volume formulas and use them to solve problems.

Analyze, compare, create, and compose shapes.

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

Apply geometric concepts in modeling situations.

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

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

Reason with shapes and their attributes.

Find arc lengths and areas of sectors of circles.

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

Define trigonometric ratios and solve problems involving right triangles.

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

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

Prove theorems involving similarity.

Apply trigonometry to general triangles.

Prove geometric theorems.

Understand and apply the Pythagorean Theorem.

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

Understand and apply theorems about circles.

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

Understand congruence in terms of rigid motions.

Make geometric constructions.

Experiment with transformations in the plane.

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

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Task
Lisa makes an octagon by successively folding a square piece of paper as follows.  First, she folds the square in half vertically and horizontally and also along both diagonals leaving these creases:
[IMG]
Next, Lisa makes four more folds, identifying each pair of adjacent lines of symmetry for the square used for the folds in the first step:
[IMG]
Finally Lisa folds the four corners of her shape along the red creases marked below:
[IMG]
Explain why the shape Lisa has made is a regular octagon.


correct_option_index: 23

24