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

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

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

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

Apply trigonometry to general triangles.

Reason with shapes and their attributes.

Understand and apply the Pythagorean Theorem.

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

Prove theorems involving similarity.

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

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

Make geometric constructions.

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

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Explain volume formulas and use them to solve problems.

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

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

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

Understand similarity in terms of similarity transformations.

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

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

Use coordinates to prove simple geometric theorems algebraically.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.
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: 3