Question

Prove that the diagonals of a rectangle are equal in length​

Answer 1

Step-by-step explanation:

Let ABCD be a rectangle.

We have to prove that AC = BD.

In the triangles ABC and DCB:

BC = CB (common)  

AB = DC   (opposite sides of a parallelogram)  

ABC =DCA = 90°   (given)

so ABC ≡ DCB (SAS)

Hence AC = DB (matching sides of congruent triangles).

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Answer 2

to prove - AC = BD

given - ABCD is a rectangle

proof - in rectangle ABCD,

             AC and BD and angle C and angle D form right angled triangles

            in ΔADC and ΔBDC,

               CD=CD ( common side)

               AD=BC ( opposite equal sides of a rectangle)

               ∠C=∠D=90° (all angles in a rectangle are 90°)

                 so by SAS congruence criterion,

                       ΔADC≅ΔBDC

                            AC = BD    (corresponding parts of congruent triangles)

                               

                                     HENCE PROVED

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