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Given : All sides of square are equal.
Step-by-step explanation:
To prove : Diagonals of square are congruent.
Let ABCD be a square. Let the diagonals AC and BD intersect each other at a point O. To prove that the diagonals of a square are equal and bisect each other at right angles, we have to prove AC = BD, OA = OC, OB = OD, and AOB = 90º.
In ABC and DCB,
AB = DC (Sides of a square are equal to each other)
ABC = DCB (All interior angles are of 90)
BC = CB (Common side)
ABC = DCB (By SAS congruency)
AC = DB (Being side of congruent triangle )
hence, Diagonals of square are congruent.
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