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

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

Apply geometric concepts in modeling situations.

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

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

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

Understand congruence in terms of rigid motions.

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

Make geometric constructions.

Prove theorems involving similarity.

Define trigonometric ratios and solve problems involving right triangles.

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

Experiment with transformations in the plane.

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

Explain volume formulas and use them to solve problems.

Understand and apply theorems about circles.

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

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

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

Reason with shapes and their attributes.

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

Understand and apply the Pythagorean Theorem.

Apply trigonometry to general triangles.

Find arc lengths and areas of sectors of circles.

Classify two-dimensional figures into categories based on their properties.
problem_activity: Task
A square is inscribed in a circle which is inscribed in a square as shown below. Note that the vertices of the inner square meet the midpoints of the outer square's sides.
[IMG]
Consider the area of the region left by removing the interior of the small square from the interior of the big square. Is the area of the blue region more or less than $\frac12$ of that?


correct_option_index: 18

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