options: Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

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

Find arc lengths and areas of sectors of circles.

Define trigonometric ratios and solve problems involving right triangles.

Use coordinates to prove simple geometric theorems algebraically.

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

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

Apply geometric concepts in modeling situations.

Prove theorems involving similarity.

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.

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.

Prove geometric theorems.

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

Analyze, compare, create, and compose shapes.

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

Apply trigonometry to general triangles.

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

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

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

Make geometric constructions.
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