At least two pairs of consecutive angles are congruent in a

Options

A. Parallelogram
B. Isosceles trapezium
C. Rhombus
D. Kite

Answer

To solve the question, we need to determine which of the given shapes has at least two pairs of consecutive angles that are congruent (equal). The shapes we are considering are a parallelogram, rhombus, kite, and isosceles trapezium.

### Step-by-Step Solution:

1. **Understand Consecutive Angles**:
Consecutive angles are angles that are adjacent to each other in a shape. For example, in a quadrilateral, angle A and angle B are consecutive angles if they share a common side.

**Hint**: Remember that consecutive angles are always next to each other.

2. **Analyze the Parallelogram**:
In a parallelogram, opposite angles are equal, but consecutive angles are supplementary (they add up to 180 degrees). Therefore, no two consecutive angles in a parallelogram are equal.

**Hint**: Check if consecutive angles can be equal or if they must add up to a certain value.

3. **Analyze the Rhombus**:
In a rhombus, like a parallelogram, opposite angles are equal, but consecutive angles are still supplementary. Thus, there are no pairs of consecutive angles that are congruent.

**Hint**: Consider how the properties of angles change when you have equal sides.

4. **Analyze the Kite**:
In a kite, there are two pairs of equal angles, but they are not consecutive. The angles between the unequal sides are equal, but the angles between the equal sides are not congruent to the other angles.

**Hint**: Look for pairs of angles that are next to each other and check their equality.

5. **Analyze the Isosceles Trapezium**:
In an isosceles trapezium, the angles adjacent to each base are equal. This means we have two pairs of consecutive angles that are congruent: one pair at the top and one pair at the bottom.

**Hint**: Identify the pairs of angles formed by the bases and see if they are equal.

6. **Conclusion**:
Based on the analysis, the isosceles trapezium is the only shape among the options that has at least two pairs of consecutive angles that are congruent.

**Final Answer**: The correct answer is the Isosceles Trapezium.