Mastering Geometry: The Same-Side Interior Angles Theorem.

Theorem 3-2 Same-Side interior Angles Theorem

If a transversal intersects two parallel lines,the same-side interior angles are supplementary

The Same-Side Interior Angles Theorem, also known as the Alternate Interior Angles Theorem, states that when two parallel lines are intersected by a transversal, the same-side interior angles formed are supplementary.

Supplementary angles are two angles that add up to 180 degrees. In this case, the angles formed inside the parallel lines on the same side of the transversal will have a sum of 180 degrees.

To apply this theorem, you must first identify the parallel lines and the transversal intersecting them. Then, look for two angles formed on the same side of the transversal, which means that they are on the same side of the parallel lines.

For example, in the diagram below, line l || m and transversal t intersects them. Angle 1 and angle 3 are same-side interior angles, as they are both inside the parallel lines and on the same side of the transversal.

“`
1 2
┌────────┐
t │ │
│ │
────┼────────┼───
│ │
│ │
└────────┘
3 4
“`

By the Same-Side Interior Angles Theorem, we know that angle 1 and angle 3 are supplementary, which means that:

angle 1 + angle 3 = 180 degrees

This theorem is useful in solving equations involving angles in geometric figures. By understanding this theorem, we can identify supplementary angles and use their relationship to simplify or solve equations.

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