Answer :
The strategy that can be used to prove that the diagonals of a parallelogram bisect each other is congruent triangles .
Given :
Let ABCD is a parallelogram with midpoint M .
To prove that he diagonals of a parallelogram bisect each other we have to go through the following steps:
Angle DBA is congruent to angle BDC.
Angle CMD is congruent to angle AMB.
Triangle CMD is congruent to triangle AMB.
Segment AM is congruent to segment MC.
M is the midpoint of segment AC.
Segment BD bisects segment AC.
Segment BM is congruent to segment MD.
M is the midpoint of segment BD.
Segment AC bisects segment BD.
Hence we have to use the concept of congruent triangles in order to prove that the diagonals of a parallelogram bisect each other.
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