Show that if the diagonals of a quadrilateral are equal and bisect each other at right
angles, then it is a square.
Answers
Answer:
It is given that the diagonals of ABCD are equal and bisect each other at right angles. Therefore, AC = BD, OA = OC, OB = OD, and ∠AOB = ∠BOC = ∠COD = ∠AOD = 90º. ... Thus, we have obtained that ABCD is a parallelogram, AB = BC = CD = AD and one of its interior angles is 90º. Therefore, ABCD is a square.
Step-by-step explanation:
Show that if the diagonals of a quadrilateral are equal and bisect each other at right
angles, then it is a square.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right
angles, then it is a square.
It is given that the diagonals of ABCD are equal and bisect each other at right angles. Therefore, AC = BD, OA = OC, OB = OD, and ∠AOB = ∠BOC = ∠COD = ∠AOD = 90º. ... Thus, we have obtained that ABCD is a parallelogram, AB = BC = CD = AD and one of its interior angles is 90º. Therefore, ABCD is a square.