Problem

A segment parallel to \(\text{one}~\text{side}\) of a triangle cuts the \(\text{other}~\text{two}~\text{sides}\). Name the theorem triggered by this configuration and state its proportional-segment conclusion.

Unworked geometric configuration showing only the supplied segment, angle, parallel, or right-angle evidence.

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What this problem is really about

The theorem’s direction is determined by what the problem gives and what it asks us to conclude. We’ll recognize the given parallel interior segment, identify the forward side-splitter theorem, compare upper and lower pieces in the same order, and contrast that logic with the converse.

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This is the converse of the side-splitter theorem because the segment is parallel to a side, so the side ratios must already be given.

This is the side-splitter theorem because a segment parallel to one side of a triangle cuts the other two sides proportionally.

This is the right-triangle altitude similarity theorem because a segment inside a triangle creates smaller triangles that look similar.

This is the angle bisector theorem because the segment splits the triangle into two smaller parts on the other sides.

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A segment parallel to \(\text{one}~\text{side}\) of a triangle cuts the \(\text{other}~\text{two}~\text{sides}\). Name the theorem triggered by this configuration and state its proportional-segment conclusion.

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