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The question asks which of the following conditions, **by itself**, is enough to guarantee that a quadrilateral is a **parallelogram**. We need to choose three correct options.

Let's analyze the options:

1. **One pair of opposite sides are parallel and congruent.**
   - This condition is sufficient by itself to guarantee that a quadrilateral is a parallelogram. **True.**

2. **One pair of consecutive sides are parallel.**
   - This condition alone is **not sufficient** to guarantee a parallelogram. **False.**

3. **Both pairs of opposite sides are pairs of parallel sides.**
   - This is the definition of a parallelogram, so this condition is sufficient. **True.**

4. **Both pairs of opposite sides are pairs of congruent sides.**
   - If both pairs of opposite sides are congruent, it guarantees a parallelogram. **True.**

5. **Its diagonals are congruent.**
   - Diagonals being congruent is a property of a rectangle, not a general parallelogram, so it’s not sufficient for a parallelogram. **False.**

### Correct choices:
1. One pair of opposite sides are parallel and congruent.
2. Both pairs of opposite sides are pairs of parallel sides.
4. Both pairs of opposite sides are pairs of congruent sides.

Would you like any more details or have further questions?

### Related Questions:
1. How do you differentiate between a rectangle and a parallelogram based on diagonals?
2. What are other sufficient conditions to determine a quadrilateral is a parallelogram?
3. How does the property of congruent sides impact the classification of quadrilaterals?
4. Can a quadrilateral with only one pair of parallel sides ever be a parallelogram?
5. What is the significance of consecutive angles in a parallelogram?

### Tip:
Remember that a parallelogram's defining property is that both pairs of opposite sides are parallel, and several conditions, like congruent sides or diagonals bisecting, are additional properties!

Which of the following conditions, by itself, is enough to guarantee that a quadrilateral is a parallelogram? Select the three correct options.

This problem involves selecting the conditions that, by themselves, are enough to guarantee that a quadrilateral is a parallelogram. Explore key geometry concepts related to parallelograms and their properties. Ideal for students in Grades 8-10.

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