options: Understand congruence in terms of rigid motions.

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

Experiment with transformations in the plane.

Find arc lengths and areas of sectors of circles.

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

Prove theorems involving similarity.

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

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.

Define trigonometric ratios and solve problems involving right triangles.

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).

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

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

Apply trigonometry to general triangles.

Analyze, compare, create, and compose shapes.

Apply geometric concepts in modeling situations.

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

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

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

Make geometric constructions.

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

Reason with shapes and their attributes.

Understand and apply theorems about circles.
problem_activity: In the following figure,
$${\overline{AE}}$$
and
$${\overline{BD}}$$
are segments.
[IMG]
a) Show that
$${{{{\triangle ABC}}}}$$
and
$${{{{\triangle CDE}}}}$$
are similar.
b) What is the scale factor of similarity transformation that takes
$${{{{\triangle ABC}}}}$$
to
$${{{{\triangle CDE}}}}$$
?
c) What is the value of the ratio of the area of
$${{{{\triangle ABC}}}}$$
to the area of
$${{{{\triangle CDE}}}}$$
? Explain how you know.
d) If the area of
$${{{{\triangle ABC}}}}$$
is
$${30\space \mathrm{cm^2}}$$
, what is the area of
$${{{{\triangle CDE}}}}$$
?


correct_option_index: 11