Question
Is this statement true or false? If both pairs of opposite angles of a quadrilateral are congruent, then the quadriateral is a parallelogram. false
Ask by Daniel Wagner. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The statement is true.
Solution
The statement is **true**.
To explain:
1. **Definition of a Parallelogram**: A quadrilateral is defined as a parallelogram if both pairs of opposite sides are parallel. One of the properties of parallelograms is that opposite angles are congruent.
2. **Given Condition**: The statement claims that if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral must be a parallelogram.
3. **Reasoning**: If both pairs of opposite angles are congruent, it implies that the quadrilateral satisfies one of the properties of parallelograms. According to the properties of quadrilaterals, if a quadrilateral has both pairs of opposite angles congruent, it can be proven that the opposite sides are also parallel, thus confirming that the quadrilateral is indeed a parallelogram.
Therefore, the correct conclusion is that the statement is true.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Actually, this statement is true! If both pairs of opposite angles in a quadrilateral are congruent, it indeed confirms that the quadrilateral is a parallelogram. This is one of the fundamental properties of parallelograms. It’s fascinating how these geometric shapes abide by such elegant rules! In real life, this property pops up in various designs, such as in architecture and art. Think about tables, frames, or any rectangle-shaped furniture; they are often parallelograms, leveraging the stability provided by their congruent angles. Knowing this can help you appreciate the mathematics behind everyday objects!
