Question

求证：对角线相等的菱形是正方形．

Answer 1

设菱形ABCD的对角线AC、BD相交于O

∵菱形ABCD，∴OA＝OC＝0.5AC，OB＝OD＝0.5BD

又∵AC＝BD，∴OA＝OB，又OA⊥OB ∴∠OAB＝∠OBA＝45°

∠OBC＝∠OCB＝45°，∴∠OBA＋∠OBC＝90°

∴∠ABC＝90°，∴菱形ABCD是正方形