Question

what values of u and v make δrst ≅ δfge?
(image of two right triangles: δrst with right angle at r, side rt labeled 9v, side rs labeled u+50; δfge with right angle at f, side fg labeled 6u, side fe labeled v+40)

Explanation:

Step1: Identify corresponding sides

Since \(\triangle RST \cong \triangle FGE\), their corresponding sides are equal. So, \(u + 50 = 6u\) (hypotenuses) and \(9v = v + 48\) (legs).

Step2: Solve for \(u\)

From \(u + 50 = 6u\), subtract \(u\) from both sides:
\(50 = 5u\)
Divide both sides by 5:
\(u = \frac{50}{5} = 10\)

Step3: Solve for \(v\)

From \(9v = v + 48\), subtract \(v\) from both sides:
\(8v = 48\)
Divide both sides by 8:
\(v = \frac{48}{8} = 6\)

Answer:

\(u = 10\), \(v = 6\)