options: Understand and apply the Pythagorean Theorem.

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

Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

Find arc lengths and areas of sectors of circles.

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.

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

Explain volume formulas and use them to solve problems.

Prove theorems involving similarity.

Reason with shapes and their attributes.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

Understand congruence in terms of rigid motions.

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

Understand and apply theorems about circles.

Define trigonometric ratios and solve problems involving right triangles.

Make geometric constructions.

Apply geometric concepts in modeling situations.

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

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

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

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

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

Analyze, compare, create, and compose shapes.

Experiment with transformations in the plane.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
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: 0

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