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explain midpoint theorem with te solving of example

Mid point theorem states that " the line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it".

⇒ ED | | BC  (Opposite sides of parallelogram are parallel)

⇒ EF | | BC

EF = DF (Proved)

⇒ EF + DF = ED = BC  (Opposite sides of the parallelogram are equal)

⇒ EF + EF = BC

⇒ 2 EF = BC

 

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The Midpoint Theorem

Figure 1 shows Δ ABC with D and E as midpoints of sides AC and AB respectively. If you look at this triangle as though it were a trapezoid with one base of BC and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids, Theorem 55.


 

 

 

 
Figure 1

The segment joining the midpoints of two sides of a triangle.

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 Δ ABC with D and E as midpoints of sides AC and AB respectively. If you look at this triangle as though it were a trapezoid with one base of BC and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids, Theorem 55. 
 

 
 
 
 
Figure 1

The segment joining the midpoints of two sides of a triangle.

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