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

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

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

Reason with shapes and their attributes.

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

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

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

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

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

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

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

Understand and apply the Pythagorean Theorem.

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Make geometric constructions.

Analyze, compare, create, and compose shapes.

Prove theorems involving similarity.

Apply geometric concepts in modeling situations.

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

Explain volume formulas and use them to solve problems.

Define trigonometric ratios and solve problems involving right triangles.

Understand and apply theorems about circles.

Apply trigonometry to general triangles.
problem_activity: Warm-up
Students examine statements deciding in each case whether the statement is always true, sometimes true, or never true. Since figures are similar if one is the result of reflecting, rotating, translating, and dilating the other, and figures are congruent only as a result of the rigid transformations, congruent figures are similar but not vice versa. Though students have not studied how angles behave under dilations, students have had multiple opportunities to see that dilations influence the size of a shape but not its angles. They also know from work in grade 7 that scaled copies have corresponding angles with the same measure, and dilations have been characterized as a process that makes scaled copies.
Launch
Display all 3 statements. Ask students to decide whether each of the statements is always, sometimes, or never true and give a signal when they have reasoning to support their decision.
Student Facing
Choose whether each of the statements is true in
all
cases, in
some
cases, or in
no
cases.
If two figures are congruent, then they are similar.
If two figures are similar, then they are congruent.
If an angle is dilated with the center of dilation at its vertex, the angle measure may change.
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
Discuss each statement one at a time with this structure:
Poll the class on their answer choice and display the answers.
If everyone agrees on one answer, ask a few students to share their reasoning, recording it for all to see.
If there is disagreement on an answer, ask students with opposing answers to explain their reasoning to come to an agreement on an answer.


correct_option_index: 4