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

Experiment with transformations in the plane.

Reason with shapes and their attributes.

Make geometric constructions.

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

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

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

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

Understand and apply the Pythagorean Theorem.

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

Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

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

Prove theorems involving similarity.

Understand and apply theorems about circles.

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

Apply geometric concepts in modeling situations.

Understand similarity in terms of similarity transformations.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

Explain volume formulas and use them to solve problems.

Apply trigonometry to general triangles.

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

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

Analyze, compare, create, and compose shapes.

Understand congruence in terms of rigid motions.

Translate between the geometric description and the equation for a conic section.
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: 19