Question

what values of u and v make (\triangle fghcong\triangle bdc)?

Explanation:

Step1: Use congruent - side property

Since \(\triangle FGH\cong\triangle BDC\), the corresponding sides are equal.
We have \(5u + 16=10u-9\) and \(v + 31=4v+13\).
For \(5u + 16=10u-9\):
Subtract \(5u\) from both sides: \(16=10u - 5u-9\).

Step2: Solve for \(u\)

Simplify \(16 = 5u-9\).
Add \(9\) to both sides: \(16 + 9=5u\), so \(25 = 5u\).
Divide both sides by \(5\): \(u=\frac{25}{5}=5\).

Step3: Solve for \(v\)

For \(v + 31=4v+13\):
Subtract \(v\) from both sides: \(31=4v - v+13\).
Simplify \(31 = 3v+13\).
Subtract \(13\) from both sides: \(31-13 = 3v\), so \(18 = 3v\).
Divide both sides by \(3\): \(v=\frac{18}{3}=6\).

Answer:

\(u = 5\), \(v = 6\)