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

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

Define trigonometric ratios and solve problems involving right triangles.

Understand congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

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

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

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

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.

Make geometric constructions.

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

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

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

Experiment with transformations in the plane.

Find arc lengths and areas of sectors of circles.

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

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

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

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

Prove geometric theorems.

Apply geometric concepts in modeling situations.

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.
problem_activity: Problem 1
The images below are maps with different scales. What do you notice? What do you wonder?
[IMG]
[IMG]
Problem 2
The map below shows Boston Common and Boston Public Garden. Perla walked around the outside perimeter of the Common and the Public Garden. About how far did she walk?
[IMG]
Problem 3
On the map below,
$${{1\over4}}$$
inch represents one mile. Candler, Canton, and Oteen are three cities on the map.
[IMG]
a.   If the distance between the real towns of Candler and Canton is 9 miles, how far apart are Candler and Canton on the map?
b.   If Candler and Oteen are
$${3 {1\over2}}$$
inches apart on the map, what is the actual distance between Candler and Oteen in miles?


correct_option_index: 8