options: Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

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

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

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

Prove theorems involving similarity.

Find arc lengths and areas of sectors of circles.

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

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

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

Apply trigonometry to general triangles.

Apply geometric concepts in modeling situations.

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

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

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

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

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

Make geometric constructions.

Experiment with transformations in the plane.
problem_activity: Warm-up
Polygons are special shapes because once we know the vertices, listed in order, we can join them by line segments to produce the polygon. This is important when performing rigid transformations. Because rigid transformations take line segments to line segments, once we track where the vertices of a polygon go, we can join them in the correct order with segments to find the image of the polygon.
In this warm-up, students begin to explore this structure, finding corresponding points in congruent polygons which are
not
vertices.
Launch
Give 3 minutes quiet think time followed by 2 minutes for a whole-class discussion.
Student Facing
Trapezoids
\(ABCD\)
and
\(A’B’C’D’\)
are congruent.
Draw and label the points on
\(A’B’C’D’\)
that correspond to
\(E\)
and
\(F\)
.
Draw and label the points on
\(ABCD\)
that correspond to
\(G’\)
and
\(H’\)
.
Draw and label at least three more pairs of corresponding points.
[IMG]
Student Response
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Anticipated Misconceptions
Students may struggle to find corresponding points that are not vertices. Suggest that they use tracing paper or the structure of the grid to help identify these corresponding points.
Activity Synthesis
Remind students that when two figures are congruent, every point on one figure has a corresponding point on the other figure.
Ask students what methods they used to find their corresponding points. Possible answers include:
Using the grid and the corresponding vertices to keep track of distances and place the corresponding point in the right place
Using tracing paper and rigid motions taking one polygon to the other


correct_option_index: 22