Question

prove that diagonals of square are equal.

Answer 1

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 (By CPCT)

the diagonals of a square are equal in length.

Answer 2

GIVEN:

            SQUARE ABCD

           DIAGONALS AC AND BD

TO PROVE:

                AC= BD

PROOF: 

                     IN TRIANGLES BAD AND ABC

                        AB = AB (COMMON)

                        AD = BC (ALL SIDES IN A SQUARE ARE EQUAL)

     ANGLE BAD = ANGLE ABC (VERTEX ANGLES, SO EQUAL)

 BY SAS,     TRIANGLE BAD IS CONGRUENT TO TRIANGLE ABC

       BY CPCT, AC = BD

                        HENCE PROVED

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