Question

the triangles are similar. identify the type of segment shown by the dashed line.
altitude
base
hypotenuse
median
find the value of the variable.
$y = \square$

Explanation:

Step1: Identify segment type

A median connects a vertex to the midpoint of the opposite side; the marked congruent sides confirm the dashed line splits the side into two equal parts, so it is a median.

Step2: Set up similarity proportion

For similar triangles, corresponding sides are proportional:
$\frac{y}{18} = \frac{y-1}{16}$

Step3: Cross-multiply to solve for y

$16y = 18(y-1)$
$16y = 18y - 18$
$18 = 18y - 16y$
$18 = 2y$
$y = \frac{18}{2}$

Answer:

D. Median
$y = 9$