Question

show that if the diagonals of a quadrilateral are equal and bisect each other at right angles then it is a square? Solve it Quickly........​

Answer 1

Step-by-step explanation:

Given :

ABCD is a quadrilateral with AC=BD,AO=CO,BO=DO,COD = 90°

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=DA

In BAD and ABC,

AD=BC (proved above )

AB=AB (common)

BD=AC (cpct)

therefore ,

BAD ≈ ABC (By SSS)

BAD+ABC = 180° (Co-interior angles)

Now,

2ABC=180° (since ABC≈BAD)

ABC =180/2

ABC =90°

Hence, the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square

Answer 2

Answer:

Explained in diagram.

Step-by-step explanation:

see the diagram. it can still be a rhombus. figure out the rest.