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

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

Experiment with transformations in the plane.

Apply trigonometry to general triangles.

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

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

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

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

Apply geometric concepts in modeling situations.

Explain volume formulas and use them to solve problems.

Understand congruence in terms of rigid motions.

Prove theorems involving similarity.

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

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

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

Reason with shapes and their attributes.

Understand and apply the Pythagorean Theorem.

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

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

Find arc lengths and areas of sectors of circles.

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

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

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

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: 2