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Q.

The diagonals of a square are equal and bisect each other at an angle of ____.

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Detailed Solution

The diagonals of a square are equal and bisect each other at an angle of 90°.
Show that the diagonals of a square are equal and bisect each other at right angles

Show that the diagonals of a square are equal and bisect each other at right angles

Let the diagonals of a square ABCD are equal and bisect each other.
Therefore, we have,
OA = OC
BA= BC (Sides of a square are equal)
OB = BO (Common)
By SSS congruency criterion, we have,

Δ A O B ≅ Δ C O B

We know corresponding sides of congruent triangles are equal.

∠ A O B = ∠ C O B (1)

Using the linear pair property, we have,

∠ A O B + ∠ C O B = 180 ° ⇒ ∠ A O B + ∠ A O B = 180 ° from eq . (1) ⇒ 2 ∠ A O B = 180 ° ⇒ ∠ A O B = 9 0 °

Therefore, the diagonals of a square are equal and bisect each other at an angle of

90 °

.
Hence, the answer is

90 °

.

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The diagonals of a square are equal and bisect each other at an angle of ____.