If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by these four lines will always be a:

Options

A. parallelogram
B. rhombus
C. square
D. trapezium

Answer

To solve the problem, we need to analyze the situation where two parallel lines are intersected by two distinct transversals. Here’s the step-by-step solution:

### Step 1: Identify the Parallel Lines
We start with two parallel lines, which we can label as line AB and line CD.

**Hint:** Remember that parallel lines never meet and are always the same distance apart.

### Step 2: Identify the Transversals
Next, we introduce two distinct transversals that cut across these parallel lines. We can label these transversals as line EF and line GH.

**Hint:** Transversals are lines that intersect two or more other lines at different points.

### Step 3: Form the Quadrilateral
The intersection of the two parallel lines (AB and CD) with the two transversals (EF and GH) creates a quadrilateral. The vertices of this quadrilateral can be labeled as points E, F, G, and H.

**Hint:** A quadrilateral is a four-sided polygon formed by connecting four points.

### Step 4: Analyze the Properties of the Quadrilateral
Now, we need to determine the properties of the quadrilateral EFGH.

- **Opposite Sides:** We observe that EF is parallel to GH (because they are both formed by the intersection of the same pair of parallel lines), while EH is not parallel to FG (since they are transversals).

**Hint:** For a quadrilateral to be a parallelogram, both pairs of opposite sides must be parallel.

### Step 5: Determine the Type of Quadrilateral
Since one pair of opposite sides (EF and GH) is parallel, but the other pair (EH and FG) is not, the quadrilateral EFGH fits the definition of a trapezium (or trapezoid in some regions), where only one pair of opposite sides is parallel.

**Hint:** A trapezium has one pair of parallel sides and the other pair is not parallel.

### Conclusion
Thus, the quadrilateral formed by two parallel lines cut by two distinct transversals is always a trapezium.

**Final Answer:** The quadrilateral formed by these four lines will always be a trapezium.