Question

to show that the diagonals of rectangle are equal to each other​

Answer 1

Step-by-step explanation:

The opposite sides of rectangles are equal. The diagonals of rectangles bisect each other. Any two adjacent angles are supplementary (obviously, since they all measure 90°) The opposite angles are equal (again, obviously, since all interior angles measure 90°)

Answer 2

The opposite sides of rectangles are equal. The diagonals of rectangles bisect each other. Any two adjacent angles are supplementary (obviously, since they all measure 90°) The opposite angles are equal (again, obviously, since all interior angles measure 90.

Theorem

The diagonals of a rectangle are equal.

Proof

Let ABCD be a rectangle.

We prove that AC = BD.

In the triangles ABC and DCB:

BC = CB (common)

AB = DC (opposite sides of a parallelogram)

angleABC =angleDCA = 90° (given)

so triangleABC ≡ triangleDCB (SAS)

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

This means that AM = BM = CM = DM, where M is the

intersection of the diagonals. Thus we can draw a single

circle with centre M through all four vertices. We can

describe this situation by saying that, ‘The vertices of

a rectangle are concyclic’.