Question

Are the diagonals of a rectangle equal? why?​

Answer 1

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Yes, the diagonals of a rectangle are equal. This is because the two diagonals are the hypotenuse of the two right angled triangles formed by the diagonals. Since, the height and base of the two triangles are equal, by Pythagoras Theorem, the hypotenuse of the triangles are also equal. Hence, the diagonals of the rectangle are equal in length.

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Answer 2

The diagonals of a rectangle are equal.

Step-by-step explanation:

[ We prove this step-by-step using Pythagoras' theorem. ]

Drawing:

First draw a rectangle ABCD, whose AB = CD and BC = AD.

We also draw the diagonals AC and BD.

Proof:

Let, AB = CD = a and BC = AD = b.

From ΔABC, we get

AB² + BC² = AC² (Pythagoras' theorem)

➜ a² + b² = AC² ... ... (1)

Again, from ΔBCD, we get

CD² + BC² = BD²

➜ a² + b² = BD² ... ... (2)

From (1) and (2), we write

AC² = BD²

➜ AC = BD, that is, the diagonals of a rectangle are equal.

Thus concluded.

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