Parallelograms Theorem 6

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Statement

The diagonals of a square are equal and perpendicular to each other.

Given:

ABCD is a square.

AC and BD are diagonals intersecting at O.

To prove:

Proof:

AB=AD (sides of a square are equal)

AB||DC (opposite sides of a square are parallel)

ABCD is parallelogram with consecutive sides equal.

ABCD is a rhombus. (by definition)

Since the diagonals of a rhombus are perpendicular to each other, AC ^ BD.

ABCD is a parallelogram.

ABCD is a rectangle with a pair of its consecutive sides equal.

Since the diagonals of a rectangle are equal, AC=BD.

Diagonal AC=Diagonal BD and AC ^ BD

Hence the theorem is proved.