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Quintin Stafford 2022-06-27 Answered
The midpoints of the sides of A B C along with any of the vertices as the fourth point make a parallelogram of area equal to what? The answer is, obviously, 1 2 area ( A B C )

In the method, I took A B C with D, E, and F as midpoints of A B, A C, and B C, respectively; and I joined D E and E F so that I get a parallelogram D E F B.
I know what the answer is because one can easily make that out. Also, those four triangles (four because the parallelogram can still be divided into two triangles and the rest two triangles add up to four) so it's simple that the area of D E B F will be 1/4 of A B C, but how?
Can anyone explain me this?
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Answers (1)

Mateo Barajas
Answered 2022-06-28 Author has 13 answers
All 4 triangles are congruent using properties of parallel lines and parallelograms and so are all equal in area. All 4 make up triangle A B C, while 2 make up parallelogram D E F B. Hence D E F B is half the area of A B C.

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