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

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.

Find arc lengths and areas of sectors of circles.

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

Define trigonometric ratios and solve problems involving right triangles.

Use coordinates to prove simple geometric theorems algebraically.

Make geometric constructions.

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

Understand and apply theorems about circles.

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

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

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

Prove geometric theorems.

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.

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

Apply geometric concepts in modeling situations.

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

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

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

Experiment with transformations in the plane.

Solve real-world and mathematical problems involving area, surface area, and volume.
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: 12