# 5.7: Properties of Midsegments

## Investigation 1

**midpoint**tool to construct the midpoints of AB and AC. Use the

**segment**tool to construct the midsegment connecting them. Measure the

**length**and

**slope**of the midsegment.

*Click the middle of a segment to measure its slope, not the endpoints*Measure the

**length**and

**slope**of BC.

## Observations

How are the **lengths** of the midsegment and BC related?
Drag a vertex of the triangle to test your hypothesis.

How are the **slopes** of the midsegment and BC related?
What does that mean about the segments? Drag a vertex of the triangle to test your hypothesis.

## Investigation 1 Directions (continued)

**midpoint**tool to construct the midpoint of BC. Use the

**segment**tool to construct the other 2 midsegments of the triangle. Measure the

**lengths**&

**slopes**of the new midsegments. Measure the

**lengths**&

**slopes**of AB and AC.

## More observations

Do your new results demonstrate the same relationships as your first measurements? Drag a vertex to test your hypothesis.

## C- 51: Triangle Midsegment Conjecture

A midsegment of a triangle is ____________________________ to the third side and _____________________ the length of the third side.

## Investigation 2

**midpoint**tool to construct the midpoints of AC and DB. Use the

**segment**tool to construct the midsegment. Measure the

**length**and

**slope**of the midsegment. Measure the

**lengths**and

**slopes**of the bases.

## Observations

How are the **slopes **of the bases related to the slope of the midsegment?
What does that mean about the segments?

What calculations can you do with the **lengths** of the bases to get the **length** of the midsegment?

## C-52: Trapezoid Midsegment Conjecture

The midsegment of a trapezoid is ________________ to the bases and equal in length to the ________________ of the bases.