Question

Which of the following statement is false?

1) The diagonals of the rectangle are congruent.
2) Diagonals of the rhombus are congruent and perpendicular to each other.
3) Opposite angles of a rhombus are ≅
4) Angles of a square are all right ∠s.

Answer 1

The false statement among the given options is that the diagonals of a rhombus are congruent and perpendicular to each other; while they are perpendicular, they are not congruent unless the rhombus is also a square.

Step-by-step explanation:

To determine which of the statements is false, let's analyze each one:

1. The diagonals of a rectangle are congruent. This statement is true; the diagonals of a rectangle are equal in length.
2. Diagonals of a rhombus are congruent and perpendicular to each other. This statement is false. While the diagonals of a rhombus are perpendicular to each other, they are not congruent (not equal in length), except in the special case when the rhombus is a square.
3. Opposite angles of a rhombus are congruent (equal). This statement is true; in a rhombus, opposite angles are equal.
4. Angles of a square are all right angles. This statement is true; a square has four right angles.

Hence, the false statement is: "Diagonals of a rhombus are congruent and perpendicular to each other."