If two parallel lines are cut by a transversal, then Same-side interior angles
When two parallel lines are cut by a transversal, several pairs of angles are formed
When two parallel lines are cut by a transversal, several pairs of angles are formed. One important type of pair is the same-side interior angles.
Same-side interior angles are a pair of angles that are on the same side of the transversal and are between the two parallel lines. These angles are also called co-interior angles or consecutive interior angles.
The key property of same-side interior angles is that they add up to 180 degrees. In other words, the sum of the measures of the two same-side interior angles is always 180 degrees.
To illustrate this, let’s consider an example. Suppose we have two parallel lines, line p and line q, and a transversal line, line t, that intersects both p and q.
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p
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t /________\ q
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In this diagram, angles 1 and 4 are same-side interior angles. Similarly, angles 2 and 3 are same-side interior angles.
Using the property mentioned earlier, we can say that angle 1 + angle 4 = 180 degrees, and angle 2 + angle 3 = 180 degrees.
This property holds true for any pair of same-side interior angles formed by the intersection of two parallel lines and a transversal.
It is important to note that same-side interior angles are not always congruent (having the same measure), unless the lines are perpendicular. For non-perpendicular parallel lines, the same-side interior angles only have a sum of 180 degrees.
Understanding the concept of same-side interior angles is helpful in solving problems involving parallel lines and transversals, as it allows us to find missing angle measures and make deductions about the relationships between angles.
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