Question

By which congruence rule is converse of midpoint theorem proved

Answer 1

In geometry , the converse of midpoint theomem is an important as the theomem itself . The converse of midpoint theomem states that :' if a line segment is drawn passing through the midpoint of any one side of triangle and parallel to any other side, then this line segment bisects the remaining third side .


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Answer 2

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side. Let us observe the figure given above. We can see the ΔABC,

Point D and E are the midpoints of side AB and side AC respectively. Also, the segment DE connects the two sides at the midpoints, then DE || BC and DE is half the length of side BC.

If we know the length of BC then it is very convenient to find the length of DE as DE is half of BC. It also allows us to find the length of sides AE, EC, BD, and DA. Since DE is parallel to BC we know that the distance between these two line segment is equal.

Also, ∠ADE = ∠ABC

So, DE || BC

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