Question
Which statement is not always true for a parallelogram? A. Consecutive angles are supplementary. B. Opposite sides are congruent. C. Diagonals bisect each other. D. It has 4 congruent angles.
Ask by Mitchell Blake. in the United States
Mar 19,2025
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Answer
D. It has 4 congruent angles.
Solution
To determine which statement is not always true for a parallelogram, let's analyze each option:
A. **Consecutive angles are supplementary.**
- This statement is true for all parallelograms. In a parallelogram, each pair of consecutive angles adds up to 180 degrees.
B. **Opposite sides are congruent.**
- This statement is also true for all parallelograms. Opposite sides of a parallelogram are always equal in length.
C. **Diagonals bisect each other.**
- This statement is true for all parallelograms. The diagonals of a parallelogram always bisect each other.
D. **It has 4 congruent angles.**
- This statement is not always true for all parallelograms. While a rectangle (a specific type of parallelogram) has 4 congruent angles, a general parallelogram does not necessarily have to have all angles equal. For example, a rhombus has opposite angles that are equal but not all four angles are congruent.
Therefore, the statement that is not always true for a parallelogram is:
**D. It has 4 congruent angles.**
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Simplify this solution Beyond the Answer
While statements A, B, and C are universally true for all parallelograms, statement D is where things get interesting! A parallelogram does indeed have 4 congruent angles, but only if it’s a special type called a rectangle. In general, a parallelogram can have unequal consecutive angles, so D is not always true! If you're ever puzzled by parallelograms again, just remember: they don't have to be perfect rectangles to be considered a parallelogram. Think of them as the versatile shape chameleons of geometry—able to take on different forms while still maintaining their fundamental properties!
