options: Experiment with transformations in the plane.

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

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

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

Reason with shapes and their attributes.

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

Understand similarity in terms of similarity transformations.

Prove geometric theorems.

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

Understand and apply theorems about circles.

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

Apply geometric concepts in modeling situations.

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

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

Apply trigonometry to general triangles.

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

Make geometric constructions.

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

Explain volume formulas and use them to solve problems.
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: 10