In quadrilateral ABCD, the diagonal AC is drawn. A line through B parallel to AC meets DC extended at E. By the same-base theorem, ar(triangle ACE) equals ar(triangle ACB) because:

B and E lie on the line BE which is parallel to AC, so triangles ACB and ACE share base AC and lie between the same parallels, giving equal areas. (This is the standard 'replace a quadrilateral by an equal-area triangle' construction.)