options: Use coordinates to prove simple geometric theorems algebraically.

Understand congruence in terms of rigid motions.

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

Prove theorems involving similarity.

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

Make geometric constructions.

Apply trigonometry to general triangles.

Apply geometric concepts in modeling situations.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Prove geometric theorems.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

Explain volume formulas and use them to solve problems.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Reason with shapes and their attributes.

Understand and apply theorems about circles.

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

Understand similarity in terms of similarity transformations.

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

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

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.
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: 22