GeoGebra Classroom

# 5.7: Properties of Midsegments

## Investigation 1

Use the 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)

Use the 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

Use the 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.