options: Reason with shapes and their attributes.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Experiment with transformations in the plane.

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

Apply geometric concepts in modeling situations.

Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

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

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

Find arc lengths and areas of sectors of circles.

Prove geometric theorems.

Explain volume formulas and use them to solve problems.

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

Define trigonometric ratios and solve problems involving right triangles.

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.

Understand and apply the Pythagorean Theorem.

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

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

Understand and apply theorems about circles.

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

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

Make geometric constructions.
problem_activity: Problem 1
In the diagram below,
$${m\parallel p}$$
.
[IMG]
a. Write three equations that are perpendicular to line
$$m$$
.
b. What is the relationship between your three equations and line
$$p$$
?
c. Find the distance between line
$$m$$
and
$$p$$
using your three equations. What do you notice?
Problem 2
In the diagram below,
$${\overleftrightarrow {AI} \parallel {\overleftrightarrow {CK}}}$$
and
$${\overleftrightarrow{IC} \perp \overleftrightarrow {AK}}$$
. How can you use the triangles
$${AHI}$$
and
$${KHC}$$
to prove that the slopes for
$${\overleftrightarrow{AI}}$$
and
$${\overleftrightarrow {CK}}$$
are the same?
[IMG]
Problem 3
Write three equations that are parellel to
$${\overleftrightarrow{AB}}$$
.
[IMG]


correct_option_index: 1