# Triangle Midsegment Theorem Worksheet

## Introduction

We will be investigating the Triangle Midsegment Theorem. This theorem says that a midsegment of a triangle is parallel to a side of the triangle and its length is half the length of that side.

## Midsegments and Side Lengths

Look at the lengths of line segments on the sides of the triangle. Do they bisect the sides of the triangle? How did you find your answer?

## Midsegments and Side Lengths

Look at the length of the midsegment in the triangle. How does that relate to the length of the side opposite from it (AC)? When considering the answer, use the lengths of AF and FC to help.

## Midsegments and Side Lengths

Move the vertices triangle to change side lengths. How does this affect the relationship between the midsegment and the side AC?

## Midsegments and Side Lengths

Continue to manipulate the triangle. Based on everything you have explored so far, would agree with the part of the theorem which states that "the midsegment is half the length of the side" will work for any triangle? Explain your reasoning.

## Midsegments Parallel to Side

How can you tell if two line (segments) are parallel using slope?

## Midsegments Parallel to Side

Look at the slope of the midsegment (m) and the slope of the side of the triangle (m1). What do you notice about the relationship between the two slopes?

## Midsegments Parallel to Side

Move the vertices of the triangles to change it. How does this affect the relationship between the two slopes?

## Midsegments Parallel to Side

Continue to manipulate the triangle. Based on everything you have explored in this section, would you say that the part of the theorem, "the midsegment is parallel to the side of the triangle," works for any triangle? Explain your reasoning.

## Putting it All Together

Consider the slopes and side lengths of the triangle and midsegments. Manipulate the triangle. Does the theorem hold true for all three midsegments even as you move the triangle? Explain your reasoning.