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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
Would the theorem of Exercise 7 remain true for a concave quadrilateral like the one shown?
To answer:
The analytic proof for the given theorem “Would the theorem of Exercise 7 remain true for the given concave quadrilateral”
Given figure is,
The above figure shows the quadrilateral.
And the theorem of Exercise 7 is “The line segments that join the midpoints of the consecutive sides of a quadrilateral form a parallelogram”
To prove “The line segments that join the midpoints of the consecutive sides of a quadrilateral form a parallelogram” for the given figure, follow as below,
The coordinates of the quadrilateral ABCD is as shown in the figure,
Let R, S, T, V are the midpoint of AB, BC, CD and AD.
Joining the R, T, TV and VR as shown in the figure.
Midpoint of AB = S =
Midpoint of AB = S =
Midpoint of AB = S =
Midpoint of BC = T =
Midpoint of BC = T =
Midpoint of BC = T =
Midpoint of CD = V =
Midpoint of CD = V =
Midpoint of CD = V =
Midpoint of AD = R =
Midpoint of AD = R =
Midpoint of AD = R =
Determining the slopes as below,
Chapter 10 Solutions
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