options: Understand congruence in terms of rigid motions.

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

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

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Define trigonometric ratios and solve problems involving right triangles.

Analyze, compare, create, and compose shapes.

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

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

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.

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

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

Prove geometric theorems.

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

Apply geometric concepts in modeling situations.

Understand similarity in terms of similarity transformations.

Prove theorems involving similarity.

Experiment with transformations in the plane.

Explain volume formulas and use them to solve problems.

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

Understand and apply the Pythagorean Theorem.

Use coordinates to prove simple geometric theorems algebraically.

Reason with shapes and their attributes.

Understand and apply theorems about circles.

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

Make geometric constructions.
problem_activity: Task
Below is a table of diameters of different denominations of United States
Coins:
| Denomination | Diameter  |
|--------------|-----------|
|     Dime     | $17.9$ mm |
|    Nickel    | $21.2$ mm |
|   Quarter    | $24.3$ mm |
| Half Dollar  | $30.6$ mm |
If we place nickels around a central dime, as in the picture below, there is room
for five nickels with extra space but not enough room for a sixth nickel:
[IMG]
How many dimes fit around a central dime?  What about around a
central nickel, quarter, or half dollar?  Do the dimes fit snugly or is there
extra space?
How many half dollars fit around a central dime?  What about around
a central nickel, quarter, or half dollar?  Do the half dollars fit snugly or
is there extra room?
Extending the work in (a) and (b) above, for positive numbers $r$ and $s$
how many circles of radius $s$ will fit around a central circle of radius $r$?


correct_option_index: 5

15