Question

Mei has a large triangular stone that she wants to divide into four smaller triangular stepping stones in a pathway. Explain why cutting along each midsegment creates four congruent stepping stones?

Answer 1

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.