Question

1. (triangle with side lengths 7, 5, 9 and a missing side marked with? and a midline or parallel segment indicated by double arrows)

Explanation:

Step1: Identify triangle side-splitter theorem

The line parallel to one side of a triangle divides the other two sides proportionally.

Step2: Set up proportional equation

Let the unknown side be $x$. The proportion is $\frac{7}{9} = \frac{5}{x}$

Step3: Solve for $x$

Cross-multiply: $7x = 9 \times 5$
$7x = 45$
$x = \frac{45}{7}$

Answer:

$\frac{45}{7}$ or approximately $6.43$