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

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

Apply trigonometry to general triangles.

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

Apply geometric concepts in modeling situations.

Define trigonometric ratios and solve problems involving right triangles.

Understand similarity in terms of similarity transformations.

Prove theorems involving similarity.

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

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

Understand and apply the Pythagorean Theorem.

Experiment with transformations in the plane.

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

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

Find arc lengths and areas of sectors of circles.

Make geometric constructions.

Prove geometric theorems.

Explain volume formulas and use them to solve problems.

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

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.

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

Reason with shapes and their attributes.

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

Use coordinates to prove simple geometric theorems algebraically.

Analyze, compare, create, and compose shapes.
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
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
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: 12