Answer:
Suppose: M, N, P, Q are the midpoints of AB, BC, CD, AD respectively
=> MNPQ is the quadrilateral inside ABCD
connect B to D, ΔABD has : M is the midpoint of AB
Q is the midpoint of AD
=> MQ is the midpoint polygon of ΔABD
=> MQ // BD and MQ = 1/2.BD (1)
ΔBCD has: N is the midpoint of BC
P is the midpoint of DC
=> NP is the midpoint polygon of ΔBCD
=> NP // BD and NP = 1/2.BD (2)
from (1) and (2) => MQ // NP ( //BD)
MQ = NP (=1/2.BD)
=> MNPQ is a parallelogram.
=> the quadrilateral inside ABCD is a parallelogram.
Step-by-step explanation:
