Question

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Answer 1

Answer:

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side. ... This theorem allows us to prove some things about the triangle.

Step-by-step explanation:

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Answer 2

Answer:

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Take a triangle ABC,E and F are the mid-points of side AB and AC resp.

Construction:-Through C,draw a line II BA to meet EF produced at D.

Proof:-

In Triangle AEF and CDF

1.AF=CF(F is midpoint of AC)

2.<AFE=<CFD (Vertically opp. angles)

3.<EAF=<DCF [Alt. angles,BA II CD(by construction) and AC is a transversal]

4.So,Triangle AEF = CDF(ASA)

5.EF=FD AND AE = CD (c.p.c.t)

6.AE=BE(E is midpoint of AB)

7.BE=CD(from 5 and 6)

8.EBCD is a IIgm [BA II CD (by construction) and BE = CD(from 7)]

9.EF II BC AND ED=BC (Since EBCD is a IIgm)

10.EF = 1/2 ED (Since EF = FD,from 5)

11.EF = 1/2 BC (Since ED = BC,from 9)

Hence,EF II BC AND EF = 1/2 BC which proves the mid-point theorem.

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