options: Experiment with transformations in the plane.

Apply trigonometry to general triangles.

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.

Find arc lengths and areas of sectors of circles.

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

Analyze, compare, create, and compose shapes.

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

Define trigonometric ratios and solve problems involving right triangles.

Use coordinates to prove simple geometric theorems algebraically.

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

Explain volume formulas and use them to solve problems.

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

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

Prove theorems involving similarity.

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

Reason with shapes and their attributes.

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

Apply geometric concepts in modeling situations.

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

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

Prove geometric theorems.
problem_activity: Activity
The purpose of this activity is for students to match relationships between angles in a figure with equations that can represent those relationships. This prepares students for writing and solving equations that represent relationships between angles in the next lesson. As students explain their reasoning, monitor for students who use the appropriate vocabulary and language (i.e. vertical angles have equal measures, supplementary angles sum to 180 degrees, etc.).
Launch
Keep students in same groups. Give students 2–3 minutes of quiet work time followed by partner and whole-class discussions.
Student Facing
Match each figure to an equation that represents what is seen in the figure. For each match, explain how you know they are a match.
[IMG]
\(g+h=180\)
\(g=h\)
\(2h+g=90\)
\(g+h+48=180\)
\(g+h+35=180\)
Student Response
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Student Facing
Are you ready for more?
What is the angle between the hour and minute hands of a clock at 3:00?
You might think that the angle between the hour and minute hands at 2:20 is 60 degrees, but it is not! The hour hand has moved beyond the 2. Calculate the angle between the clock hands at 2:20.
Find a time where the hour and minute hand are 40 degrees apart. (Assume that the time has a whole number of minutes.) Is there just one answer?
Student Response
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for free access to Extension Student Response.
Activity Synthesis
The goal of this discussion is for students to articulate the angle relationships they noticed in each figure and equation. Display the figures for all to see. Select previously identified students to share their explanations for each figure. If not mentioned in students’ explanations be sure that students see the vertical, supplementary, straight, and right angle relationships in the figures.


correct_option_index: 25