options: Apply geometric concepts in modeling situations.

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

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

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.

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

Explain volume formulas and use them to solve problems.

Understand similarity in terms of similarity transformations.

Experiment with transformations in the plane.

Apply trigonometry to general triangles.

Reason with shapes and their attributes.

Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.

Find arc lengths and areas of sectors of circles.

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

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

Understand congruence in terms of rigid motions.

Prove geometric theorems.

Define trigonometric ratios and solve problems involving right triangles.

Use coordinates to prove simple geometric theorems algebraically.

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

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

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

Make geometric constructions.

Prove theorems involving similarity.

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

Analyze, compare, create, and compose shapes.
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: 1