Discovering the Magic of Triangle Midsegments

A midsegment of a triangle joins the midpoints of two sides. It is always parallel to the third side and exactly half its length, which is what makes it useful for finding missing measurements without trigonometry.

• It is parallel to the third side of the triangle (the side it doesn’t touch).
• Its length is half the length of the third side of the triangle.

Worked examples: finding a triangle midsegment

Practice questions on triangle midsegments

1. Triangle ( JKL ) has sides (JL = 12 text{ cm} ), (JK = 9 text{ cm} ), and (KL = 15 text{ cm} ). Determine the length of the midsegment connecting the midpoints of sides (JL ) and (KL ).
2. If the midsegment of triangle (MNO ) is (11 text{ cm} ), and it connects the midpoints of sides (MN ) and (NO ), find the length of side (MO ).

1. The midsegment parallel to (JK ) will have a length of ( frac{15}{2} = 7.5 text{ cm} ).
2. (MO ) will be ( 2 times 11 = 22 text{ cm} ).

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