How To Find The Length Of A Midsegment In A Triangle: Step-By-Step Guide With Example.

Midsegment

a segment that joins the midpoints of two sides of the triangle

A midsegment is a line segment joining the midpoints of two sides of a triangle. It is always parallel to the third side of the triangle and half the length of the third side.

To find the length of a midsegment, you first need to identify the two sides of the triangle that the midsegment is joining. Then, you can find the midpoint of each of those two sides by taking the average of their endpoints. Finally, you can use the distance formula to find the length of the midsegment by finding the distance between the two midpoints.

For example, if a triangle has sides of length 8, 10, and 12, you could find the length of the midsegment connecting the midpoints of the 8- and 10-side as follows:

1. Find the midpoint of the 8-side: (0 + 4, 0 + 0)/2 = (2, 0)
2. Find the midpoint of the 10-side: (4 + 8, 0 + 6)/2 = (6, 3)
3. Use the distance formula to find the length of the midsegment: √[(6 – 2)² + (3 – 0)²] = √40 = 2√10

Therefore, the midsegment connecting the midpoints of the 8- and 10-side of this triangle has a length of 2√10 units.

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