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Midsegments
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Vocabulary
• Midsegment – The segment connecting the midpoint of the sides of a triangle, also the segment connecting the legs of a trapezoid
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Investigation
• Get your supplies– 1 piece of patty paper to be cut in two (1 piece
of paper and a marker)– Straight Edge
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Midsegment Investigation
Patty Paper (Regular Paper and marker)• Draw a large triangle on a piece of patty paper• Fold/Pinch each of the sides to find the midpoint• Connect all three midpoints, so you have a
triangle drawn with four triangles inside
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Midsegment Investigation
• Use a second sheet of patty paper to copy the entire triangle, including the midsegments
• Compare all four triangles• What conclusions can you
draw?
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Midsegment Conjecture
• The three midsegments of a triangle divide the triangle into four congruent triangles
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Midsegment Investigation
• Mark all congruent angles in the triangles.
What conclusions can be made about the direction (slope) of the two highlighted lines?
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Midsegment Investigation
• Mark all congruent angles in the triangles.
What conclusions can be made about the length of the two highlighted lines?
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Triangle Midsegment Conjecture
• A midsegment of a triangle is parallel to the third side, and half the length of the third side
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Trapezoid Midsegment Investigation
• 2 pieces of patty paper• Draw a small trapezoid on the left side of
your patty paper.• Find the midsegment of the non parallel
sides
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Trapezoid Midsegment Investigation
• Label the angles 1,2,3 & 4 as shown• Copy everything onto the second piece of
patty paper
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Trapezoid Midsegment Investigation
• Compare angles 1 & 3 and angles 2 & 4
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Trapezoid Midsegment Investigation
• On the original drawing, extend the longest base
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Trapezoid Midsegment Investigation
• Add the length of the shorter base onto the extended longer base
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Trapezoid Midsegment Investigation
• How many times does the midsegment fit onto this extended base (the sum of the two bases)?
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Trapezoid Midsegment Conjecture
• The midsegment of a trapezoid is parallel to the bases and equal in length to half the sum of the bases.
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Trapezoid Midsegment Conjecture
• If we use software to shrink a base to a point, the trapezoid becomes a triangle. Will the same formula work for the triangle midsegment conjecture?
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Practice Problems
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Practice Problems