Question

1. what values of b and c make \\( \triangle xyz \cong \triangle sut \\)?

Explanation:

Step1: Use the property of congruent triangles (corresponding sides are equal)

Since \(\triangle XYZ\cong\triangle SUT\), then \(XY = SU\) and \(XZ=ST\), \(YZ = UT\).
We have \(XY = 45\), \(SU = 5b\), so \(5b=45\).

Step2: Solve for \(b\)

Divide both sides of the equation \(5b = 45\) by \(5\): \(b=\frac{45}{5}=9\).

Step3: Use the other pair of corresponding sides

We know \(ST = 5\), \(XZ\) is not labeled with a variable in terms of \(c\) (assuming \(YZ = UT\)), \(YZ=5c\), \(UT = 15\), so \(5c=15\).

Step4: Solve for \(c\)

Divide both sides of the equation \(5c = 15\) by \(5\): \(c=\frac{15}{5}=3\).

Answer:

\(b = 9\), \(c=3\)