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

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

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

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

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

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

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

Analyze, compare, create, and compose shapes.

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

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

Prove theorems involving similarity.

Define trigonometric ratios and solve problems involving right triangles.

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

Experiment with transformations in the plane.

Apply trigonometry to general triangles.

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

Understand similarity in terms of similarity transformations.

Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

Make geometric constructions.

Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.
problem_activity: Problem 1
Two lines intersect at the origin, as shown in the coordinate plane below.
[IMG]
a.   What is the relationship between
$${{\angle AEC}}$$
and
$${\angle DEB}$$
? Between
$${{\angle AEC}}$$
and
$${\angle AED}$$
?
b.   Use transformations to show that
$${{\angle AEC}}$$
is congruent to
$${\angle DEB}$$
.
Problem 2
In the diagram below, lines
$$a$$
and
$$b$$
are parallel. Line
$$c$$
is a transversal that cuts through the parallel lines.
[IMG]
a.   Name four pairs of congruent vertical angles.
b.
$$\angle 2$$
and
$$\angle 8$$
are congruent. How can you prove this?
c.   Name three other pairs of corresponding angles.


correct_option_index: 0