CBSE Class 9 Answered

Figure shows a square ABCD . AC and BD are diagonals that meet at centre O.

ΔDAB and ΔCBA are right angled triangles that have right angles at A and B .

For the right angled triangles ΔDAB and ΔCBA,

AB is coomon side and AD = BC ( sides of square ) .

Hence , ΔDAB and ΔCBA are congruent . Hence  AC = BD , i.e. digaonals of square are equal.

Since ΔDAB is right angled isocless triangle, ∠ADO = 45^o . Similarly ∠CDO = 45^o .

In the ΔADO and ΔCDO ,

∠ADO = ∠CDO

side DO is common abd sides DA and DC are equal .

Hence , ΔADO and ΔCDO are congruent .

Hence corresponding angles ∠AOD = ∠COD are equal . 

Also ∠AOD and ∠COD are adjacent angles on a line . Hence ∠AOD = ∠COD = 90^o .

Hence diagonals of square are perpendicular to each other .