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

Define trigonometric ratios and solve problems involving right triangles.

Make geometric constructions.

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

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

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

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

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

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

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

Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

Experiment with transformations in the plane.

Reason with shapes and their attributes.

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply theorems about circles.

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

Explain volume formulas and use them to solve problems.

Understand congruence in terms of rigid motions.

Apply geometric concepts in modeling situations.

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

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Prove theorems involving similarity.

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

Find arc lengths and areas of sectors of circles.
problem_activity: Narrative
In this activity, students identify right triangles. They also explain why certain given shapes are not right triangles. As they determine whether a triangle is a right triangle, students may use the corner of an index card or a piece of paper, use a protractor, or trace an angle in a triangle to compare with an angle elsewhere that they know to be a right angle. In doing so, students practice choosing tools strategically (MP5).
Required Materials
Materials to Gather
Index cards
Patty paper
Protractors
Launch
Groups of 2
Provide access to index cards, patty paper, and protractors.
Activity
5 minutes: independent work time
2 minutes: partner discussion
Monitor for students who use tools to check angles and those who estimate them visually. Ask the latter: “How might we check that the angles that look like right angles are
\(90^\circ\)
?”
Student Facing
Identify all shapes that are right triangles. For each right triangle, mark the right angle with a small square.
[IMG]
Explain why the other shapes are not right triangles.
Student Response
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Advancing Student Thinking
Students may not identify triangles C or D because of the orientation.
Consider asking:
“How can we show that a triangle has a right angle?”
“Where else do you see triangles that may have perpendicular sides?”
“What tools could you use to see if each triangle has any right angles?”
Activity Synthesis
Invite students to share their responses and how they found the right triangles in the set.
“Were there any triangles that appeared to be right triangles but are not, or don’t appear to be right triangles but are?” (Triangle H looks like one but isn’t.)


correct_option_index: 4