Which of the following statements is not true ?

Concept: A parallelogram is a rectangle exactly when each of its angles is 90°; since a parallelogram's opposite angles are always equal and consecutive angles are always supplementary, forcing all four angles equal automatically forces each to be 90°. A rectangle is a square exactly when all four sides are also equal. A rhombus is a square exactly when all four angles are also equal, which (by the same supplementary-angle rule, since a rhombus is a parallelogram) again forces each angle to be 90°. A kite (two pairs of adjacent equal sides) has, purely from its own diagonal symmetry, one pair of opposite angles always equal — so "making the kite's opposite angles equal" can only add new information about the other pair. Forcing that second pair equal as well forces the kite's two unequal side-lengths to become equal too, producing a rhombus. Neither reading of the condition — the already-equal pair alone, or both pairs together — forces a right angle anywhere, so neither reading turns a kite into a rectangle.

Application: Checking each statement against this rule: the parallelogram-to-rectangle, rectangle-to-square, and rhombus-to-square statements all match the condition exactly, so all three are true. The kite-to-rectangle statement does not, under either reading of "opposite angles equal": taken as the pair that is already automatically equal in every kite, it adds nothing and guarantees no new shape; taken as both pairs together, it only forces the kite's two side-lengths to match, giving a rhombus, never a right angle. Either way, a kite with equal opposite angles is not thereby a rectangle, so this is the statement that is not true.

Contrast: checking each shape's own condition:

• Parallelogram becomes a rectangle when all its angles are equal — true, because equal angles under the parallelogram angle rule can only occur at 90° each.

• Rectangle becomes a square when all its sides are equal — true, since a rectangle already has right angles, so equal sides complete the square.

• Rhombus becomes a square when all its angles are equal — true, since a rhombus already has equal sides, so equal (hence 90°) angles complete the square.

• Kite becomes a rectangle when its opposite angles are equal — false under either reading: taking only the pair that is already equal in every kite adds no new condition, and taking both pairs equal only forces the kite's two side-lengths to match, giving a rhombus; neither reading forces a 90° angle anywhere.

Cross-check: take a kite with vertex angles 100°, 80°, 100°, 80° in order (sum = 360°). Both pairs of opposite angles are equal (100° = 100° and 80° = 80°), and all four sides become equal, so the kite is a rhombus — yet no angle is 90°, so it is not a rectangle. This confirms that the kite-to-rectangle statement is the untrue one.