Parallel Lines and Transversals

When two lines are intersected by a transversal, several pairs of angles are formed. These pairs of angles can be classified based on their relative positions and measurements. One specific case is when the corresponding angles are equal. Let's explore this further to understand why the correct answer is option 'A' - parallel.

Corresponding Angles

When a transversal intersects two lines, it forms eight angles. Corresponding angles are pairs of angles that are in the same relative position at each intersection. In other words, they are on the same side of the transversal and in corresponding positions at each intersection. Corresponding angles are denoted by the same letter or symbol.

Key Point: Corresponding angles are formed when a transversal intersects two lines and are in the same relative position at each intersection.

Equal Corresponding Angles

The given statement states that any pair of corresponding angles are equal. This means that all corresponding angles formed by the transversal and the two lines are equal in measure. If this condition is satisfied, it indicates a specific geometric relationship between the lines.

Parallel Lines

When two lines are intersected by a transversal and all corresponding angles are equal, it implies that the lines are parallel. This is a fundamental property of parallel lines and is known as the Corresponding Angles Postulate.

Key Point: If a transversal intersects two lines and all corresponding angles are equal, then the lines are parallel.

Explanation

When corresponding angles are equal, it means that the lines are parallel. This is because if the lines were not parallel, the corresponding angles would have different measures. By satisfying the condition of equal corresponding angles, the lines must be parallel.

Therefore, the correct answer is option 'A' - parallel.

Then the lines are parallel