Below are graphs of three triangles and their midpoints. The vertices for the base of each triangle and the endpoints of the midsegment are listed below:

• Triangle 1: A (-4,3), C (2,1), and D (0,5), E (3,4)
• Triangle 2: A (-4,7), C (-2,1), and D (-1,7), E (0,4)
• Triangle 3: A (-3,1), C (4,1), and D (-2,4), E (2,4)

On your own paper copy and complete the table below the graphs finding the slope of the base and midsegment of each triangle.

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	Slope of base AC	Slope of midsegment DE
Triangle 1	numerator 1, denominator 3 1 3	numerator 1, denominator 3 1 3
Triangle 2	-3	-3
Triangle 3	0	0

Based on the results of your data, what appears to always be true about the relationship between the slope of the midsegment of a triangle and the slope of its bases? Record your answer in your notes.

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The slopes are the same, which makes the midsegment always parallel to the bases of a triangle.

Below are graphs of three trapezoid and their midsegments. The vertices for both bases and the end points of the midsections of each trapezoid are listed below:

• Trapezoid 1: A (-3,3), B (-3,6) and D (5,1), C (5,8); E (1,7), F (1,2)
• Trapezoid 2: A (-3,-1), B (1,5) and D (5,-1), C (5,5); E (-1,2), F (5,2)
• Trapezoid 3: A (-1,3), B (4,8) and D (1,1), C (4,4); E (0,2), F (4,6)

On your own paper copy and complete the table below the graphs finding the slope of each base and midsegment of each trapezoid.

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	Slope of base 1	Slope of base 2	Slope of midsegment EF
Trapezoid 1	Undefined	Undefined	Undefined
Trapezoid 2	0	0	0
Trapezoid 3	1	1	1

Based on the results of your data, what appears to always be true about the relationship between the slope of the midsegment of a trapezoid and the slope of its bases?

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The slopes are the same, which makes the midsegment always parallel to the bases of a trapezoid.

In the following triangles and trapezoids, you will be given the equation of the line containing a base or a midsegment. Use what you know about how midsegments are related to the sides of their figures to find the requested information. Record your answer.

Determine the equation of the line containing the midsegment that doesn't intersect side AB.

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y = 3 over 4 3 4 x − 3.5

Determine the equation of the line containing the midsegment of trapezoid ABCD.

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y= -x + 4.5

Determine the equation of the line containing side AC.

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y = 1 over 10 1 10 x − 2

Determine the equations of the line containing the bases of trapezoid ABDE.

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y = 3 over 4 3 4 x + 1   and   y = 3 over 4 3 4 x − 7