options: 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.

Understand congruence in terms of rigid motions.

Understand and apply the Pythagorean Theorem.

Understand similarity in terms of similarity transformations.

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

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

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

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

Find arc lengths and areas of sectors of circles.

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

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

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

Apply trigonometry to general triangles.

Prove geometric theorems.

Reason with shapes and their attributes.

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

Apply geometric concepts in modeling situations.

Understand and apply theorems about circles.

Explain volume formulas and use them to solve problems.

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

Make geometric constructions.

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

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.
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: 2