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

Reason with shapes and their attributes.

Make geometric constructions.

Apply trigonometry to general triangles.

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

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

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

Understand similarity in terms of similarity transformations.

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

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

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

Prove geometric theorems.

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

Understand and apply theorems about circles.

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

Understand and apply the Pythagorean Theorem.

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

Use coordinates to prove simple geometric theorems algebraically.

Define trigonometric ratios and solve problems involving right triangles.

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

Experiment with transformations in the plane.

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

Analyze, compare, create, and compose shapes.

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

Understand congruence in terms of rigid motions.
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: 8