Custom Search

Geometry > Challenging problems

Challenging geometry problems: square

  1. P is any point on diagonal BD of square ABCD. From P, perpendiculars PE and PF are drawn to sides BC and CD.
    Prove that EF = AP

     
  2. In square ABCD, E and F are midpoints of sides AD and CD. BE and AF intersect at G.
    Prove that CG = CB


     
  3. In square ABCD, AE bisects angle CAD, intersecting side CD at E. CF is drawn perpendicular to AE, meeting AE extended at F.
    Prove that CF = ½ AE


     
  4. P is a point in square ABCD. The measures of angle PBC and angle PCB are 15°.
    Prove that triangle APD is equilateral.


     
  5. Three identical squares are placed side by side as shown in the figure below.
    Prove that ∠DBG + ∠EBG + ∠HBG = 90°