## What Makes a Triangle a Triangle?

## Opening

# What Makes a Triangle a Triangle?

- What do you know about this figure?
- What makes a triangle a triangle?

- What do you know about this figure?
- What makes a triangle a triangle?

Build triangles and explore the angle relationships in triangles.

Start with a sheet of paper. Fold the left edge toward the center at a slant. Unfold. Fold the right edge toward the center so that the fold overlaps the first fold you made. Unfold. Fold the bottom edge toward the center so that the fold overlaps the first two folds you made. Unfold.

Look at the figure that is outlined by the folds.

- What type of figure is this? How do you know? Why do you think this figure was formed as a result of folding the paper the way you did?
- Measure each of the three angles inside the figure and write the measurements on the paper. What do you notice?
- For each of the three angles you measured, there are three angles that share the same vertex but lie outside the figure. What is the sum of these three angles? How do you know?

- What is the sum of the angles in your triangle?
- Check with other students nearby. What is the angle sum in their triangles?

On the same sheet of paper, choose a corner and fold it toward the center. Unfold.

Look at the figure outlined by the edges of the paper and the fold.

- What type of figure is this? How do you know?
- Measure each of the angles. What do you notice?

On a new sheet of paper, using your protractor and its ruler side, draw triangles with the following characteristics:

- Has one obtuse angle.

What is the largest angle measure possible for the obtuse angle? What can you conclude? - Has two obtuse angles.

What do you notice? What can you conclude? - Has side lengths of 3 inches, 4 inches, and

6 inches. - Has side lengths of 3 inches, 4 inches, and

8 inches. What can you conclude?

Explain how you constructed different types of triangles. Use your work to support your explanation.

- Assume you were given two sides of a triangle. How many possible triangles can you draw?

Take notes about your classmates' conclusions and explanations for their triangles.

As your classmates' present, ask questions such as:

- When you added up the angle measures, did the sum come to exactly 180°? Explain.
- What is the sum of the angle measures in a triangle?
- Why can’t a triangle have two obtuse angles?
- Within one triangle, what is the largest measure that the sum of angles can be?

Write a summary about the angles in a triangle.

Check your summary:

- Do you say what the sum of the angle measures in a triangle is?
- Do you explain why it is impossible for a triangle to have two obtuse angles?
- Do you discuss what makes the shape of a triangle?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**I think a triangle is similar to a quadrilateral because ...**