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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
In Exercises 1 to 17, complete an analytic proof for each theorem.
The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.
To answer:
The analytic proof for the given theorem “The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side”.
Given theorem is,
The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.
The above figure shows the triangle ABC.
The vertices of the triangle ABC is A
D and E are the midpoints of the sides AC and BC.
Now, joining the points D and E as shown in the figure.
Hence, the line DE is parallel to the third side of the triangle AB.
Based on the midpoint formula,
The midpoint of AC
The midpoint of AC
Similarly, midpoint of BC
The midpoint of BC
Based on the distance formula, the length of DE which has the coordinates of D
DE
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