options: Experiment with transformations in the plane.

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

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

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

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

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

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

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

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.

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

Use coordinates to prove simple geometric theorems algebraically.

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

Reason with shapes and their attributes.

Prove geometric theorems.

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

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Make geometric constructions.

Understand and apply theorems about circles.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.
problem_activity: Task
Suppose $\triangle ABC$ and $\triangle DEF$ share three corresponding congruent sides as pictured below:
[IMG]
Show that $\triangle ABC$ is congruent ot $\triangle DEF$ as follows:
Apply a translation to move $\triangle ABC$ to $\triangle A^\prime B^\prime C^\prime$ with $A^\prime = D$.
Apply a rotation to move $\triangle A^\prime B^\prime C^\prime$ to $A^{\prime \prime}B^{\prime \prime}C^{\prime \prime}$ with $A^{\prime \prime} = D$ and $B^{\prime \prime} = E$.
Explain why $\left|A^{\prime \prime}C^{\prime \prime}\right| = \left|DF\right|$ and conclude that $\overleftrightarrow{DE}$ is the perpendicular bisector of $\overline{C^{\prime \prime}F}$.
Show that reflection over $\overleftrightarrow{DE}$ maps $F$ to $C^{\prime \prime}$ and conclude that $\triangle ABC$ is congruent to $\triangle DEF$.


correct_option_index: 10