options: Understand and apply the Pythagorean Theorem.

Apply trigonometry to general triangles.

Prove theorems involving similarity.

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

Reason with shapes and their attributes.

Understand congruence in terms of rigid motions.

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

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

Analyze, compare, create, and compose shapes.

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.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Use coordinates to prove simple geometric theorems algebraically.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

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

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

Explain volume formulas and use them to solve problems.

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

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

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

Prove geometric theorems.

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

Graph points on the coordinate plane to solve real-world and mathematical problems.
problem_activity: Activity
In this activity students use trigonometry to calculate the measure of an angle when given two sides of a right triangle. Then they apply a method of their choosing to calculate other side lengths and angle measures in the triangle.
Monitor for students who use:
the Pythagorean Theorem
multiple trigonometric equations
the Triangle Angle Sum Theorem
Launch
“Don’t forget to calculate 3 measurements per triangle.”
Students need not complete all the problems before the discussion.
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select 2 of the 3 questions to complete. Chunking this task into more manageable parts may also support students who benefit from additional processing time.
Supports accessibility for: Organization; Attention; Social-emotional skills
Student Facing
Find all missing side and angle measures.
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Student Response
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Activity Synthesis
Tell students there are at least 3 different methods for solving these problems:
Pythagorean Theorem
multiple trigonometric equations
the Triangle Angle Sum Theorem
Invite students to rank the methods in order of most to least preferred and tell them to be prepared to share their reasoning. After 1 minute of quiet think time ask a few students to share. Tell the class that there is no one best method; personal preference and the specific problem both influence your choices.
Speaking: MLR8 Discussion Supports.
To support students in producing statements about the methods they preferred for solving the problems, provide sentence frames for students to use when they share. For example, “I prefer _____ because _____,” or  “_____ was better because _____.”
Design Principle(s): Support sense-making


correct_option_index: 18