Question

pqrs is a square with midpoints x and y of sides RS and PQ respectively. diagonal SQ intersects XY at O . show that area of triangle SOX = area of triangle YOQ

Answer 1

Taking yq and six as parallel and sq as transversal,
Angle yoq= Sox (vertically opp.)
Angle y = x = 90°
Therefore triangle yoq is similar to triangle xos
As yq = sx, all sides will be equal and hence the triangles will be congruent. So the areas will be equal