Question

1. what values of a and b make \\( \triangle uvw \cong \triangle fge \\)?

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle UVW\cong\triangle FGE\), corresponding sides are equal. So \(VW = GE\) and \(UW=FE\).

Step2: Solve for \(a\)

Given \(VW = 13\) and \(GE=a + 4\). Set up the equation \(13=a + 4\).
Subtract 4 from both sides: \(a=13 - 4\).
So \(a = 9\).

Step3: Solve for \(b\)

Given \(UW=b + 30\) and \(FE = 40\). Set up the equation \(b+30=40\).
Subtract 30 from both sides: \(b=40 - 30\).
So \(b = 10\).

Answer:

\(a = 9\), \(b = 10\)