options: Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.

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

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

Apply trigonometry to general triangles.

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

Reason with shapes and their attributes.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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.

Explain volume formulas and use them to solve problems.

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.

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

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).

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

Analyze, compare, create, and compose shapes.

Understand similarity in terms of similarity transformations.

Make geometric constructions.

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

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Prove geometric theorems.
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: 3