Name:

Mike Callinan

To solve the triangle inside a rectangle presented below:

A triangle has two shared vertices and one shared side with a rectangle.

The third vertex is anywhere on the side opposite of the shared side (see

figures above).

How does the area of the triangle compare with the area of the rectangle?

Why do you think this relationship holds?

Extensions

Where would you move the third vertex of the triangle to have a minimum

perimeter? Explain why this position results in a minimum perimeter.

**Conjecture/Hypothesis/Prediction:**

We felt the area of the large triangle would be half the area of the rectangle.

**Procedures/Materials**

Using Geosketchpad we constructed a rectangle with a triangle inside that had two shared vertices and one shared side with the rectangle. We found the area the large triangle and found its ratio to the total area of the rectangle. See below:

**Conclusion (analysis using technology and understanding why it works)**

We concluded our hypothesis was true that the area of the triangle is half the area of the rectangle.

**Comments and reactions (what did I learn)**

I learned this would be an
excellent activity for sixth grade students to reinforce this concept in
Geometry.

**Extensions (what other questions can I ask or explore?)**

Link to my Twotriangle GSP file