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

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

Understand and apply the Pythagorean Theorem.

Use coordinates to prove simple geometric theorems algebraically.

Experiment with transformations in the plane.

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

Reason with shapes and their attributes.

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

Define trigonometric ratios and solve problems involving right triangles.

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

Apply geometric concepts in modeling situations.

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

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

Understand similarity in terms of similarity transformations.

Analyze, compare, create, and compose shapes.

Understand and apply theorems about circles.

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.

Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

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

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

Make geometric constructions.

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

Apply trigonometry to general triangles.

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

Explain volume formulas and use them to solve problems.
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: 11