Question

prove that the diagnols of the square bisect each other at 90 and are equal

Answer 1

So, the diagnols of the square bisect each other at 90 and are equal...

Answer 2

Hi friend here is your answer

_____________________________

Given - - -
ABCD a square with point of diagonal intersection be O

TPT (To prove that)
1)The diagonals of square are equal i.e AC = BD

2)Bisect each other at right angle


Proof - -

In triangle ABC and triangle DBC

AB = DC (Sides of all square are
equal)

Angle ACB = Angle DCB
( Both will be 90 degrees)

Side BC = Side BC (Common side)


Therefore both the triangles are congruent by S-A-S test

Therefore AC = BD proved diagonals are equal in length


In triangle AOB and triangle COD

Angle AOB = Angle COD


Angle ABO = Angle CBO

Hence both the triangles are congruent by A-A test

Hence AO = CO and OB = OD


Hence diagonals of square bisect each other

_____________________________

Hope it helps you...............!!
#The Usos