Section 5.4 Theorem – MIDSEGMENT THEOREM The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

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Section 5.4 Theorem – MIDSEGMENT THEOREM The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

How to prove is a segment is a midsegment Sketch the triangle/plot the points Use the midpoint formula to find the midpoints of the sides Use the slope formula to find the slopes of the potential midsgements and opposite sides Confirm that the slopes of the potential midsegment and the side are the same Use the distance formula to calculate the length of the possible midsegment and opposite side Confirm the length of the potential midsegment is half as long as the opposite side x1+ x2 , y1+ y2 2 2 Distance Formula: The midpoint formula: AB = √ (x2 – x1)2 + (y2 – y1)2