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

Prove theorems involving similarity.

Understand and apply theorems about circles.

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

Understand congruence in terms of rigid motions.

Make geometric constructions.

Use coordinates to prove simple geometric theorems algebraically.

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

Apply trigonometry to general triangles.

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

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

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

Experiment with transformations in the plane.

Apply geometric concepts in modeling situations.

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

Understand and apply the Pythagorean Theorem.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Understand similarity in terms of similarity transformations.

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

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.
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: 4