## Types of Triangles

## Opening

# Types of Triangles

Discuss the following with your classmates.

- Triangles can be classified by the size of their angles.
- Triangles can also be classified according to the lengths of their sides.

Discuss the following with your classmates.

- Triangles can be classified by the size of their angles.
- Triangles can also be classified according to the lengths of their sides.

Explore the properties of triangles.

Use the Triangles Sketch interactive to explore equilateral, isosceles, scalene, acute, obtuse, and right triangles.

- For each triangle that is classified by sides, state everything you notice about the angles.
- For each triangle that is classified by angles, state everything you notice about the sides.
- Use the Exterior Angles button. What do you notice about the relationship of the exterior angles to the interior angles for each type of triangle?

INTERACTIVE: Triangles Sketch

- How are the angles in each figure related? What do the angles tell you about the figure?
- For each triangle classified by sides, what do you notice about the angles?
- Do any of the triangles that are classified by angles also have one of the characteristics of triangles that are classified by sides?
- What is the sum of the interior angles for each triangle?
- How does the sum of two of the angles compare to the measure of the third angle?
- If one of the angles is a right angle, what is the sum of the other two angles?

Use the Making Triangles interactive to explore how the lengths of the sides determine whether you can construct a triangle.

- Start with a base length of any size. Make the sum of the length of the other two sides less than the base length. Can you make a triangle? Explain why.
- Start with a base length of any size. Make one of the sides longer than the base. Can you make a triangle? Explain why.

Using the explorations you just did, generalize:

- If you were given the length of 3 sides, how could you determine if those 3 lengths would make a triangle?
- If you were given 3 angles, how could you determine if those 3 angles would make a triangle?

INTERACTIVE: Making Triangles

- If you add the lengths of two of the sides, what do you know about the relationship between this sum and the length of the third side?
- Can you move a side to the other side and make another triangle?
- If you choose two angles, what conditions will allow you to make a triangle?
- What conditions will not allow you to make a triangle?
- If the one side does not change, what side lengths will not make a triangle?

List your conclusions about the properties of triangles. Provide examples to illustrate your conclusions.

- Why do the angles in a triangle add up to 180°?

This figure may help you explain your thinking. Note that lines *a* and *b* are parallel.

Take notes about your classmates’ conclusions regarding the angles and sides of a triangle.

As your classmates present, ask questions such as:

- When you added the angle measures, was the sum exactly 180°? Explain.
- How do you think angle measures and side lengths are related in triangles?
- What is true for all triangles?
- If a triangle has complementary angles, what kind of triangle is it?
- Could a side of a triangle be parallel to another side?
- If you know the lengths of two sides, what can you tell about the length of the third side?

Watch the video to see Karen and Maya discussing the different tools they use to construct triangles.

- What did Karen and Maya find out about different tools?
- What tools were most appropriate for what problems?
- How would you know which tools you might select to help you solve the problems?

VIDEO: Mathematical Practice 5

Write a summary about the angles and sides in triangles.

Check your summary:

- Do you explain the relationship of the angles in a triangle?
- Do you explain what conditions (number of sides, angles measures, and so on) will/won’t allow you to make a triangle?

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

**Something I wonder about triangles is…**