Quadrilaterals

Opposite sides are equal, All angles are 90°, Diagonals are equal

A rectangle has opposite sides equal, all angles 90°, and diagonals equal. However, all sides need not be equal (that would be a square).

Opposite sides are equal, Diagonals bisect each other, One pair of opposite sides is parallel and equal, Opposite angles are equal

Tests for parallelogram include: opposite sides equal, diagonals bisect each other, one pair of opposite sides parallel and equal, and opposite angles equal. All sides equal is a test for rhombus, not just parallelogram.

6√2 cm

In a square with side 'a', diagonal = a√2. Here, side = 6 cm, so diagonal = 6√2 cm. Using Pythagorean theorem: d² = 6² + 6² = 72, so d = √72 = 6√2 cm.

115°

In a parallelogram, adjacent angles are supplementary. ∠W + ∠X = 180°. So ∠X = 180° - 65° = 115°.