how to verify mid point theroum using paper cutting and pasting activity?

Mid-point theorem can be verified using paper cutting and pasting method as follows:

1. Cut a triangle from a piece of paper and name it as ABC.

2. Mark the mid points, D and E of the two sides of this triangle say AB and AC respectively.

2. Join D and E.

3. Measure the lengths of the line segments DE and BC, you will find that DE = BC.

4. Also, measure the angle ADE and angle ABC, you will find that both these angles are equal, which means that DE || BC.

Thus, mid-pointy theorem is verified.

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Make any triangle ABC.
take the mid points of line segments ab and ce as d and e.
now, the Triangle ade is formed, u take another piece of paper and cut it out of the same size as that of triangle ade.
place this new triangle adjacent to the lower part of the side ac on triangle abc.
place that new triangle in such a way that its vertices are ec and f. f being the new vertice, the one not touching any part of triangle abc.
now, we know that triangle ade is congruent to triangle cef since ,
angle aed is equal to angle cef ; vertically opposite
ae = ce ; e is the mid point of ac
angle dae=angle fce ; alternate angles equal between parallel lines cf and ab. ab being the triangle abc's side and cf being the triangle ecf's side.
so, by a.a.s. axiom they are congruent.
you know how to prove bdcf a parallelogram naa?since bd and cf are equal and opposite sides.

then you can easily verify the mid point theorem by these two pieces of paper triangles.
hope this is what u wanted.

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