options: Analyze, compare, create, and compose shapes.

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

Reason with shapes and their attributes.

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Make geometric constructions.

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

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.

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

Define trigonometric ratios and solve problems involving right triangles.

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

Experiment with transformations in the plane.

Apply geometric concepts in modeling situations.

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

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

Explain volume formulas and use them to solve problems.

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

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Understand and apply theorems about circles.

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

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
problem_activity: Warm-up
This activity invites students to think carefully about the definition of congruence. Students can use any rigid motion to demonstrate all points are congruent.
Student Facing
If
\(A\)
is a point on the plane and
\(B\)
is a point on the plane, then
\(A\)
is congruent to
\(B\)
.
Try to prove this claim by explaining why you can be certain the claim must be true, or try to disprove this claim by explaining why the claim cannot be true. If you can find a counterexample in which the “if” part (hypothesis) is true, but the “then” part (conclusion) is false, you have disproved the claim.
Student Response
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Activity Synthesis
Invite students to share. If students only suggest translation, ask if it is possible to use another transformation. If rotation is not mentioned by students, there is no need to continue to push for that solution.


correct_option_index: 20