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Answer :
Final answer:
Two lines that are cut by a transversal are parallel if the sum of any pair of interior angles on the same side of the transversal is 180 degrees.
Explanation:
To determine if two lines are parallel when intersected by a transversal, we can use the property of interior angles. When a transversal intersects two parallel lines, it creates several pairs of corresponding angles. One key property is that the sum of any pair of interior angles on the same side of the transversal is always equal to 180 degrees.
Let's consider two lines, line AB and line CD, intersected by transversal EF. Now, let's focus on the interior angles formed on the same side of transversal EF. If we label these angles as angles 1, 2, 3, and 4, we can see that:
Angle 1 + Angle 2 = 180 degrees (since they are supplementary angles).
Angle 3 + Angle 4 = 180 degrees (also supplementary).
If lines AB and CD are parallel, this relationship will hold true for any pair of interior angles on the same side of transversal EF. In other words, the sum of these angles will always equal 180 degrees.
So, in summary, two lines that are cut by a transversal are parallel if the sum of any pair of interior angles on the same side of the transversal is 180 degrees. This property is a fundamental concept in geometry and is used to identify parallel lines in various geometric problems.
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