Answer : Explained.
Step-by-step explanation: As given in the question and shown in the attached figure, ΔABC be the large triangular stone that Mei wants to divide into four smaller triangular stepping stones in a pathway.
Let D, E and F be the mid-points of the sides BC, CA and AB respectively. Then, DE, EF and FD are the mid-segments of ΔABC.
Then , we have
4 × Area of ΔDEF = 4 ×Area of ΔFBD = 4 × ΔAFE = 4 × Area of ΔECD = Area of ΔABC.
Thus, we have
ΔDEF ≅ ΔFBD ≅ ΔAFE ≅ ΔECD.
Thus, in this way, cutting along mid-segments creates four congruent stepping stones.
