options: Experiment with transformations in the plane.

Prove theorems involving similarity.

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

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

Understand and apply theorems about circles.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

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

Make geometric constructions.

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

Analyze, compare, create, and compose shapes.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

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

Reason with shapes and their attributes.

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

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

Understand and apply the Pythagorean Theorem.

Explain volume formulas and use them to solve problems.

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

Apply trigonometry to general triangles.

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.
problem_activity: Task
In triangles $ABC$ and $DEF$ below $m(\angle A) = m(\angle D)$, $m(\angle B) = m(\angle E)$ and $|\overline{AB}| = |\overline{DE}|$.
[IMG]
Find a sequence of translations, rotations, and reflections which maps $\triangle ABC$ to $\triangle DEF$.
After working on problem (a), Melissa says
Since $m(\angle A) = m(\angle D)$ and $m(\angle B) = m(\angle E)$ then I also know that $m(\angle C) = m(\angle F)$. So these triangles share all three angles and this is enough to know that they are congruent. I don't need to be told that $|\overline{AB}| = |\overline{DE}|$.
Is Melissa correct that $m(\angle C) = m(\angle F)$? Explain.
Is she right that two triangles sharing three pairs of congruent angles are always congruent? Explain.
Below are two triangles which share three congruent angles: $m(\angle P) = m(\angle T)$, $m(\angle Q) = m(\angle U)$, $m(\angle R) = m(\angle V)$:
[IMG]
Show that, after applying a suitable dilation, $\triangle PQR$ is congruent to $\triangle TUV$.


correct_option_index: 24