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

Analyze, compare, create, and compose shapes.

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

Reason with shapes and their attributes.

Find arc lengths and areas of sectors of circles.

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

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

Understand congruence in terms of rigid motions.

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

Apply geometric concepts in modeling situations.

Apply trigonometry to general triangles.

Make geometric constructions.

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

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

Experiment with transformations in the plane.

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

Understand and apply theorems about circles.

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.

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

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

Explain volume formulas and use them to solve problems.

Understand and apply the Pythagorean Theorem.

Define trigonometric ratios and solve problems involving right triangles.

Graph points on the coordinate plane to solve real-world and mathematical problems.
problem_activity: Problem 1
Figure 1 (F1) and Figure 2 (F2) are shown below. For each statement below, determine if it is true or false. Explain your reasoning.
[IMG]
a.   A reflection over the
$$x$$
-axis and a translation to the left will transform F1 to F2, making the two figures congruent.
b.   A rotation of
$${180^{\circ}}$$
about the origin will transform F1 to F2, making the two figures congruent.
c.   A dilation from the origin and a translation up will transform F1 to F2, making the two figures similar.
d.   A reflection across the
$$x$$
-axis and a reflection across the
$$y$$
-axis will transform F1 to F2, making the two figures congruent.
e.   There is no sequence that will transform Figure 1 to Figure 2, making the two figures neither congruent nor similar.
Problem 2
The pentagon shown below is the resulting image of pentagon
$${ABCDE}$$
after it was dilated from point
$$A$$
by a scale factor of
$${\frac{1}{2}}$$
and then rotated clockwise
$${90^{\circ}}$$
about point
$$A$$
.
What are the original coordinates of pentagon
$${ABCDE}$$
?
[IMG]


correct_option_index: 21