Which of the following statements is not always true?
A.
In a rhombus, the diagonals bisect opposite angles.
B.
In a rhombus, the diagonals are perpendicular.
C.
In a rhombus, the diagonals are congruent.
D.
In a rhombus, all four sides are congruent.
To determine which statement is not always true for a rhombus, we need to understand the properties of a rhombus.
A rhombus is a quadrilateral with four sides of equal length. It also has the property that opposite angles are equal.
Let's evaluate each statement to determine if it is always true for a rhombus:
A. In a rhombus, the diagonals bisect opposite angles.
This statement is always true for a rhombus. The diagonals of a rhombus intersect at a right angle, bisecting the opposite angles.
B. In a rhombus, the diagonals are perpendicular.
This statement is always true for a rhombus. The diagonals of a rhombus intersect at a right angle, making them always perpendicular.
C. In a rhombus, the diagonals are congruent.
This statement is always true for a rhombus. The diagonals of a rhombus are equal in length and intersect at their midpoints, creating congruent line segments.
D. In a rhombus, all four sides are congruent.
This statement is always true for a rhombus. All four sides of a rhombus are equal in length.
So, by the process of elimination, the statement that is not always true for a rhombus is option A: "In a rhombus, the diagonals bisect opposite angles." The diagonals of a rhombus bisect the opposite angles, but this may not be true for other quadrilaterals.