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

Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

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

Explain volume formulas and use them to solve problems.

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

Make geometric constructions.

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.

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

Apply geometric concepts in modeling situations.

Understand similarity in terms of similarity transformations.

Apply trigonometry to general triangles.

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

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

Define trigonometric ratios and solve problems involving right triangles.

Understand and apply the Pythagorean Theorem.

Experiment with transformations in the plane.

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

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

Reason with shapes and their attributes.

Understand congruence in terms of rigid motions.
problem_activity: Narrative
In this activity, students identify and sketch angles in their environment—in the text, graphics, and shapes in their physical surroundings—and reinforce the idea of an angle as a figure made up of two rays that share an endpoint.
In future lessons, students will look more closely at the properties of angles and consider how they can be measured and whether the length of the segments that form them impacts the size of the angles.
Required Materials
Materials to Gather
Rulers or straightedges
Launch
Groups of 2
Give each student a ruler or a straightedge.
Activity
5 minutes: independent work time
2 minutes: partner discussion
Student Facing
Here are two figures.
[IMG]
Find 2–3 angles in each figure. Draw pairs of rays to show the angles.
Sketch a part of your classroom that has 2–3 angles. Draw pairs of rays to show the angles.
Student Response
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Advancing Student Thinking
Students may say they have identified an angle because they have found a vertex. Ask these students to explain what they mean and to describe the angle they see. Consider asking:
“How do you see the rays that share this vertex? Can you draw them?”
“Could more than one angle share a vertex? How could you use figure A from the previous activity to explain?”
Activity Synthesis
“How did you find the angles?” (We looked for intersections of segments. When the segments meet or cross, angles are formed.)
“Where is the vertex of each angle you found?”


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