options: Understand and apply theorems about circles.

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

Reason with shapes and their attributes.

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

Understand congruence in terms of rigid motions.

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

Explain volume formulas and use them to solve problems.

Apply geometric concepts in modeling situations.

Experiment with transformations in the plane.

Understand and apply the Pythagorean Theorem.

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

Prove geometric theorems.

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

Define trigonometric ratios and solve problems involving right triangles.

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

Make geometric constructions.

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

Understand similarity in terms of similarity transformations.

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

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

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

Find arc lengths and areas of sectors of circles.

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

Apply trigonometry to general triangles.

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

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Problem 1
All the circles below have congruent radii, but different centers.
What polygons can you create from the marked points in the following figure?
Describe the features of each polygon, and use the properties of circles to justify your reasoning.
[IMG]
Problem 2
Margi has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her calico cat? Use the scale drawing of Margie’s room shown below, together with (only) a compass and straight edge. Place an M where Mack will be if the theory is true.
[IMG]
Problem 3
The cats changed positions. Mack left the room. Simon and JoJo also moved but stayed the same distance apart. Draw two new locations for Simon and JoJo.
[IMG]


correct_option_index: 8

15