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

Understand similarity in terms of similarity transformations.

Define trigonometric ratios and solve problems involving right triangles.

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.

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

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

Prove geometric theorems.

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

Experiment with transformations in the plane.

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

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

Understand and apply the Pythagorean Theorem.

Analyze, compare, create, and compose shapes.

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

Find arc lengths and areas of sectors of circles.

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

Apply geometric concepts in modeling situations.

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

Prove theorems involving similarity.

Make geometric constructions.

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

Apply trigonometry to general triangles.

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

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

Understand and apply theorems about circles.
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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