Show that the diagonals of a …

Let ABCD be a square When diagonals are constructed we get two triangle that is ∆ ADC and ∆ BCD We have to prove that these triangles are congruent (same) to justify that diagonals are equal. In ∆ADC and ∆ BCD AD =BC (sides) DC =DC (common) Angle ADC = angle BCD (90) So ∆ADC is congruent to ∆BCD AC =BD (CPCT :- coresponding part of congruent triangle ) AC and BD are diagonals of square ABCD In same square let us take the ∆AOD and ∆BOC Note:- here O is the intersection point of diagonals of square In ∆AOD and ∆BOC AD = BC Angle ADO = Angle OBC Angle DAO =Angle OCB (Alternative interior angle) ∆AOD and ∆BOC are congruent AO = OC (CPCT) DO = OB (CPCT) Hence diagonals bisect each other Same way when we prove ∆AOD is congruent to ∆DOC using SSS congruence rule we will get Angle AOD = Angle DOC (CPCT)---------- note 1 let angle AOD = angle 1 let angle DOC = angle 2 When we add angle 1 and 2 we will get 180° Angle 1 + Angle 2 = 180° From note 1 Angle 1= angle 2 So, angle 1+ angle 1 = 180° 2(angle 1) = 180° Angle 1 = 90° Angle 1, angle 2 = 90° Hence diagonals of a square are equal and bisect each other at right angle Hope you got it!!! ☺️☺️