Lecture
A square is a rectangle in which all sides are equal.
The square has the following properties:
1. the square has all the corners right;
2. the diagonals of the square are equal;
3. The diagonals of the square intersect at a right angle and are the bisectors of its angles.
AB = BC = CD = DA
∠ A = ∠ B = ∠ C = ∠ D = 90 °
AC ⊥ BD
AC = BD
Theorem.
If the diagonals of the rectangle intersect at a right angle, then this rectangle is a square.
Evidence.
The rectangle is a parallelogram, and a parallelogram whose diagonals intersect at right angles is a rhombus. Then the rhombus all sides are equal. So we have a rectangle in which all sides are equal, and by definition this is a square. The theorem is proved
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