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Below is a proof of the statement "if a line is parallel to one side of a triangle and intersects the other two sides at distinct points, then it separates these sides into segments of proportional lengths." Use the given triangle to answer the question. proof and triangle Which reason justifies Step 2? Question 17 options: Vertical angles are congruent. Corresponding angles are congruent. Alternate interior angles are congruent. Alternate exterior angles are congruent.

User Lvolmar
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Final answer:

The justification for Step 2 of the proof is that 'Alternate interior angles are congruent'. This concept is used when a line parallel to one side of a triangle intersects the other sides, forming congruent angles with the larger triangle and leading to proportional segments.

Step-by-step explanation:

The question concerns a geometric proof dealing with a line parallel to one side of a triangle, intersecting the other two sides. When a line is drawn parallel to one side of a triangle, it creates a smaller, similar triangle within the original triangle. As such, the sides are in proportion due to the properties of similar triangles.

Step 2 of the proof likely involves establishing an angle relationship that arises from the parallel line. The most appropriate choice to justify this step, without the specific details of the proof, would be that 'Alternate interior angles are congruent'. This is because when a line is parallel to one side of a triangle and intersects the other two sides, it forms angles with those sides that are congruent to angles of the larger triangle, due to the parallel lines.

If the question were specifically about the angles formed at the points where the line intersects the non-parallel sides, we would use the concept of alternate interior angles to establish the necessary congruency conditions. The congruency of alternate interior angles is one of the reasons the segments formed are proportional in length.

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