Question

a triangle with a line segment parallel to the base, creating a smaller triangle at the top. the left sides of the triangles have one tick mark (indicating congruence), the right sides have two tick marks (indicating congruence). the length of the top segment of the trapezoid (the line parallel to the base) is labeled x, and the length of the base of the larger triangle is labeled 3x - 15.

Explanation:

Step1: Identify Midline Theorem

The triangle has a midline (the segment with length \( x \)) parallel to the base (\( 3x - 15 \)). By the Midline Theorem, the midline length is half the base length. So, \( 3x - 15 = 2x \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 3x - 2x - 15 = 0 \), which simplifies to \( x - 15 = 0 \). Then add 15 to both sides: \( x = 15 \).

Answer:

\( x = 15 \)