Answer + Step-by-step explanation:
a.
The converse of the Theorem :
In a triangle ,a line that passes through the midpoint of one side and parallel to another side, bisects the third side.
b.
In the triangle PMR :
• T is the midpoint of the side PR.
• TU // MR
Then (according to The converse of the midpoint theorem)
PU = UM
In the triangle PNM :
• U is the midpoint of the side PM.
• US // MN
Then (according to The converse of the midpoint theorem)
PS = SN
In the triangle NMP :
• S is the midpoint of the side PN.
• QR // PM
Then (according to The converse of the midpoint theorem)
MR = RN
In the quadrilateral PQNP ,the two diagonals QR and PN bisects each other
Hence , PQNP is a parallelogram .
