**Show that the diagonals of a square are equal and bisect each other at right angles.**

**Solution:**

Let's suppose that we are given a square ABCD with diagonals AC and BD.

In and , we have

**(Alternate Interior angles)**

AB=CD **(Sides of square are equal)**

**(Alternate Interior angles)**

Therefore, **by ASA congruence rule**,

It means that we have AO=CO and BO=DO **(1)**

**(Corresponding parts of congruent triangles are equal) **

In and

AO=AO ** (Common)**

AB=AD ** (Sides of square are equal)**

OB=OD ** (Proved above)**

Therefore, **by SSS congruence rule**,

**(Corresponding parts of congruent triangles are equal) (2)**

But, we also have **(Linear pair) (3)**

Using equation **(2)** in equation **(3)**, we get

** (4)**

Similarly, ** (5)**

From **(1),** **(4) and (5)**, we can say that diagonals of a square are equal and bisect each other at right angles.