Finding the Slopes and Relationship of a Triangle Midsegment

Learn how to find the slopes of a triangle's midsegment and its corresponding third side using coordinate geometry to determine if they are parallel.

Answer

Identify the coordinates of the endpoints of the midsegment (the blue line segment):
The endpoints are and .
Calculate the slope of the midsegment using the slope formula :
Identify the coordinates of the endpoints of the third side (the side not connected to the midsegment):
The third side connects the points and .
Calculate the slope of the third side:
Compare the slopes:
Since both slopes are equal (), the lines are parallel.

Both slopes are

, and there is a parallel relationship.

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Finding the Slopes and Relationship of a Triangle Midsegment

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