The midpoints form four congruent triangles

 

Consider the outer triangles sides labeled A, B, C. After finding the midpoints of the sides, let the lengths be represented by a,a,b,b,c,c. After labeling each side it is easier to visualize the congruence relation.

To confirm your visual assumption consider the measurements taken during construction.

Notice that the small triangles have equal measures.

Therefore, we can conclude they are congruent.

 

See triangle picture

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