Question

corresponding angles form when a transversal intersects with two parallel lines.
true
false

Explanation:

Step1: Recall the definition of corresponding angles.

Corresponding angles are formed when a transversal intersects two lines (they don't have to be parallel, but when the lines are parallel, corresponding angles are equal). However, the formation of corresponding angles is when a transversal cuts two lines (parallel or not). Wait, no—actually, the question is about when they form. Wait, no, the statement is "Corresponding angles form when a transversal intersects with two parallel lines." But actually, corresponding angles are formed whenever a transversal intersects two lines (parallel or non - parallel). But wait, no—let's check the definition. Corresponding angles are pairs of angles that are in the same relative position at each intersection where a straight line (transversal) crosses two others. So they form when a transversal intersects two lines (regardless of being parallel). But the statement says they form only when the two lines are parallel. That's incorrect? Wait, no—wait, maybe I got it wrong. Wait, no—actually, the formation of corresponding angles is a result of a transversal intersecting two lines (parallel or not). But the property that corresponding angles are equal is when the lines are parallel. But the question is about when they form. So if a transversal intersects two non - parallel lines, corresponding angles still form (they just aren't equal). So the statement "Corresponding angles form when a transversal intersects with two parallel lines" is false, because they form when a transversal intersects any two lines, not just parallel ones. Wait, no—maybe the question is a bit tricky. Wait, let's re - examine. The definition: Corresponding angles are created where a transversal crosses two (usually parallel) lines. But actually, the intersection of a transversal with two lines (parallel or not) creates corresponding angles. So the statement implies that they only form when the lines are parallel, which is not true. So the answer should be False? Wait, no—wait, maybe I made a mistake. Wait, no—let's think again. If we have two non - parallel lines and a transversal, do corresponding angles exist? Yes. For example, draw two non - parallel lines and a transversal. At each intersection, the angles in the same relative position (like top - left, top - left) are corresponding angles. So they form regardless of the lines being parallel. So the statement that they form only when the lines are parallel is false. So the correct answer is False? Wait, no—wait, maybe the question is worded differently. Wait, the question is "Corresponding angles form when a transversal intersects with two parallel lines." So the claim is that the formation of corresponding angles is conditional on the two lines being parallel. But since corresponding angles form whenever a transversal intersects two lines (parallel or not), the statement is false.

Step2: Evaluate the statement.

The statement says that corresponding angles form only when the transversal intersects two parallel lines. But as we know, corresponding angles are formed when a transversal intersects any two lines (parallel or non - parallel). So the statement is false.

Answer:

False