give tow angle rules that can only be used when we have parallel line and an intersecting line ?
When we have parallel lines and an intersecting line, we can use two angle rules known as the corresponding angles rule and the alternate interior angles rule.
1. Corresponding Angles Rule:
When a transversal intersects two parallel lines, the corresponding angles that are formed are congruent. Corresponding angles are the angles that are on the same side of the transversal and in the same relative position (i.e., one pair is formed on the same side of the lines, while the other pair is formed on the other side). In other words, if Line 1 and Line 2 are parallel, and Line 3 is the transversal intersecting them, then the corresponding angles formed by Line 1 and Line 3 will be congruent to the corresponding angles formed by Line 2 and Line 3.
2. Alternate Interior Angles Rule:
When a transversal intersects two parallel lines, the alternate interior angles that are formed are congruent. Alternate interior angles are the angles that are on opposite sides of the transversal and in the interior of the parallel lines. In other words, if Line 1 and Line 2 are parallel, and Line 3 is the transversal intersecting them, then the alternate interior angles formed by Line 1 and Line 3 will be congruent to the alternate interior angles formed by Line 2 and Line 3.
Remember that these rules rely on the assumption that the lines are parallel and the given transversal intersects them. If the lines are not parallel or the transversal does not intersect them, these angle rules might not be applicable.