If the diagonals of the quadrilateral are equal and bisect each other at right angles, then it is a square has been proved below.
What is a triangle?
A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right angle triangle, equilateral triangle, and much more.
Suppose diagonal are ab ac and db
Let's say Δ aob and Δcob
Now oa and oc will be the same so oa = oc
Since diagonal intersecting at the right angle so ∠aob= ∠cob
So,
Δaob ≅ Δcob
So,
ab = cb
Now,
Δaob ≅ Δdoa,
And,
Δboc ≅ Δcod
So,
ad = ab and cb = dc
So,
ab = bc = cd = da
Since all sides are equal so it must be a square.
Hence " If diagonal bisect at the right angle then it will be square".
For more about triangles,
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