Answer:
This is called a mid segment theorem in which the al ine segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side.
Step-by-step explanation:
Suppose we have a triangle ABC. Then the midpoints can be located as D, E and F. If we join D , E and F another triangle is formed.
From the figure we can see that
AE≅ CE
AD≅DB
BF≅CF
BECAUSE all the given points are the midpoints which divide the lines into two equal halves.
If we increase the line DE to a point L we find out that DL is parallel to BC i.e. it does not meet at any point with BC. ( the two lines do not meet)
(1)
If we join C with L we find out that the the line DE is half in length to the line BC.
AS
AE= CE (midpoints dividing into equal line segements.)
LE= DE
Triangle CEL= Triangle DEF
so
DL= BC
But DE = 1/2 DL
therefore
DE= 1/2 BC (2)
Therefore from 1 and 2 we find that a line segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side
