# Triangle Midsegment: Guided Exploration

## DIRECTIONS:

1) Use the MIDPOINT tool to plot the midpoints of any 2 sides of the given triangle.
2) Use the SEGMENT tool to draw the segment (triangle midsegment) connecting these 2 points.
3) Use the SLOPE tool to measure the slope of the midsegment and the slope of the side of the
triangle the midsegment doesn't touch. Then select the MOVE tool . Drag

*A, B*, and*C*around.## 4)

What do you notice about these two slopes? What does this imply about the midsegment and the side of the triangle this midsegment doesn't touch? Explain.

5) Measure and display the name and value of the midsegment. (To do so, click on the midsegment so the
style bar appears. Then select the

**AA**icon. The check**Show Label**and**Show Value**). Do the same for the side of the triangle this midsegment doesn't touch. The name of the midsegment should be**f**. The name of the triangle side this midsegment doesn't touch should be**g**. 6) In the "Steps" window, type**f/g**. What is this value? Now move*A*,*B*, and*C*around. What do you notice about the value of the ratio**f/g**?## 7)

From your observations, how does the length of a triangle midsegment compare with the length of the side fo the triangle it doesn't touch?

## 8)

Use YET ANOTHER TOOL to verify what you claimed in your response to question (4). How does this help illustrate your response to (4) is indeed true?