Lesson 8

Triangles with 3 Common Measures

Let’s contrast triangles.

8.1: 3 Sides; 3 Angles

Examine each set of triangles. What do you notice? What is the same about the triangles in the set? What is different?

Set 1:

A set of 6 triangles with varied attributes.  Please ask for additional assistance.

Set 2:

A set of 4 triangles with varied attributes. Please ask for additional assistance.

8.2: 2 Sides and 1 Angle

Examine this set of triangles.

As set of 9 triangles with some common angles and side.  Please ask for assistance.
  1. What is the same about the triangles in the set? What is different?
  2. How many different triangles are there? Explain or show your reasoning.

8.3: 2 Angles and 1 Side

Examine this set of triangles.

A set of 8 triangles with varied attributes. Please ask for additional assistance.
  1. What is the same about the triangles in the set? What is different?
  2. How many different triangles are there? Explain or show your reasoning.

Summary

Both of these quadrilaterals have a right angle and side lengths 4 and 5:

Two quadrilaterals each with two given side lengths labeled 4 and 5, and a right angle.


However, in one case, the right angle is between the two given side lengths; in the other, it is not.

If we create two triangles with three equal measures, but these measures are not next to each other in the same order, that usually means the triangles are different. Here is an example:

Two triangles.