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<h2 style="font-weight: bold; margin: 12px 0;">What are same-side interior angles?</h2>Same-side interior angles, also known as consecutive interior angles, are a pair of angles formed when a transversal intersects two parallel lines. These angles are located on the same side of the transversal and inside the region bounded by the two parallel lines.

<h2 style="font-weight: bold; margin: 12px 0;">How do you prove angles are same-side interior?</h2>To prove that two angles are same-side interior angles, you need to establish two key conditions. First, demonstrate that the angles are formed by a transversal intersecting two parallel lines. This often involves showing that corresponding angles are congruent or alternate interior angles are congruent. Second, verify that the angles are located on the same side of the transversal and within the region enclosed by the two parallel lines.

<h2 style="font-weight: bold; margin: 12px 0;">What is the same-side interior angles theorem?</h2>The same-side interior angles theorem states that if a transversal intersects two parallel lines, then the pairs of same-side interior angles are supplementary. In other words, the measures of the two same-side interior angles add up to 180 degrees. This theorem is a fundamental concept in Euclidean geometry and is frequently used in geometric proofs and problem-solving.

<h2 style="font-weight: bold; margin: 12px 0;">Are same-side interior angles always congruent?</h2>No, same-side interior angles are not always congruent. In fact, they are only congruent in a special case where the transversal is perpendicular to the parallel lines. In all other cases, same-side interior angles are supplementary, meaning their measures add up to 180 degrees.

<h2 style="font-weight: bold; margin: 12px 0;">Why are same-side interior angles supplementary?</h2>The fact that same-side interior angles are supplementary can be understood by considering the properties of parallel lines and transversals. When a transversal intersects two parallel lines, it creates several angle pairs with specific relationships. For instance, corresponding angles are congruent, and alternate interior angles are also congruent. These relationships, combined with the fact that angles on a straight line add up to 180 degrees, lead to the conclusion that same-side interior angles must be supplementary.

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