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

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

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

Make geometric constructions.

Experiment with transformations in the plane.

Prove theorems involving similarity.

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

Define trigonometric ratios and solve problems involving right triangles.

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Reason with shapes and their attributes.

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

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

Explain volume formulas and use them to solve problems.

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

Find arc lengths and areas of sectors of circles.

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

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.

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

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.
problem_activity: Task
Below is an isosceles triangle $ABC$ with $|AB| = |AC|$:
[IMG]
Three students propose different arguments for why $m(\angle B) = m(\angle C)$.
Ravi says
If I draw the bisector of $\angle A$ then this is a line of symmetry for $\triangle ABC$ and so $m(\angle B) = m(\angle C)$.
Brittney says
If $M$ is the midpoint of $\overline{BC}$ then $\triangle ABM$ is congruent to $\triangle ACM$ and so $\angle B$ and $\angle C$ are congruent.
Courtney says
If $P$ is a point on $\overline{BC}$ such that $\overleftrightarrow{AP}$ is perpendicular to $\overline{BC}$ then $\triangle ABP$ is congruent to $\triangle ACP$ and so $\angle B$ and $\angle C$ are congruent.
Fill in the details in each argument to show why $m(\angle B) = m(\angle C)$. Can you find another different argument showing that $m(\angle B) = m(\angle C)$?


correct_option_index: 24