Question

prove that line segment joining the-mid point of two sides of a triangle is parallel to the third side and equal to half of it .plzz answer

Answer 1

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. 
Proof:Consider the triangle ABC with the midpoint of  AB labelled M.

Now construct a line through M parallel to BC.

Label the point of intersection of this line with BC by P.

Now construct a line through M parallel to AC.

Label the point of intersection of this line with AC by QClaim: AMP is congruent to MBQ.  why?

AM=BM [midpoint].< AMP = <MBQ [Corresponding angles for parallel lines cut by an transversal].

<BQM=<QCP=<APM [Corresponding angles for parallel lines cut by an transversal].

<BMQ=<MAP [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]

AMP is congruent to MBQ. [ASA]

Therefore: AP=MQ=PC and MP=BQ=QC. 

Since midpoints are unique, and the lines connecting points are unique, the proposition is proven.

HOPE THAT HELPS YOU MARK BRAINLIEST

Answer 2

Thus so
Its a mid point thereom .
And it can be proved by
. proving the triangles congruent and then by construction its converse .