Question

find the values of x and y.
(image of a triangle with a midline segment, labeled with expressions: x + 3, \\(\frac{3}{2}x + 2\\), 2y - 1, 3y - 5)

Explanation:

Step1: Solve for x (Midline Theorem)

The segment is a midline, so \( x + 3=\frac{3}{2}x + 2 \).
Subtract \( x \) and 2: \( 1=\frac{1}{2}x \).
Multiply by 2: \( x = 2 \).

Step2: Solve for y (Congruent Segments)

Sides \( 2y - 1 \) and \( 3y - 5 \) are congruent: \( 2y - 1 = 3y - 5 \).
Subtract \( 2y \) and add 5: \( 4 = y \).

Answer:

\( x = 2 \), \( y = 4 \)