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

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

Understand and apply the Pythagorean Theorem.

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Find arc lengths and areas of sectors of circles.

Reason with shapes and their attributes.

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

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

Experiment with transformations in the plane.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

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

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

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Apply trigonometry to general triangles.

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

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

Make geometric constructions.

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

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.
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