In the diagram below of AABC, D, E, and F are the midpoints of AB, BC, and CA, respectively. C A F D E B What is the ratio of the area of ACFE to the area of ACAB? (1) 1:1 (2) 1:2 (3) 1:3 (4) 1:4
【Explanation】: In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and is half its length. This means that the line segment joining the midpoints of two sides of a triangle divides the triangle into four smaller triangles of equal area. Therefore, the area of triangle CFE is one-fourth the area of triangle CAB. Hence, the ratio of the area of triangle CFE to the area of triangle CAB is 1:4.
