Q: 5 Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
Given : ABCD is a quadrilateral with AC=BD,AO=CO,BO=DO,COD =
To prove: ABCD is a square.
Proof: Since the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a rhombus.
Thus, AB=BC=CD=D
In BAD and
ABC,
AD=BC (proved above )
AB=AB (common)
BD=AC
BAD
ABC (By SSS)
(CPCT)
BAD+
ABC =
(Co-interior angles)
2. ABC =
ABC =
Hence, the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.