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

Apply geometric concepts in modeling situations.

Understand and apply theorems about circles.

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

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.

Make geometric constructions.

Find arc lengths and areas of sectors of circles.

Define trigonometric ratios and solve problems involving right triangles.

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

Explain volume formulas and use them to solve problems.

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

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

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

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

Apply trigonometry to general triangles.

Prove geometric theorems.

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

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

Reason with shapes and their attributes.

Understand congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.

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

Understand and apply the Pythagorean Theorem.
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: 21