Question

what values of a and b make (\triangle xyzcong\triangle vwu)?

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle XYZ\cong\triangle VWU\), the corresponding sides are equal. So, \(5a + b+24=7b\) and \(8b - 14=3b + a\).

Step2: Simplify the first equation

From \(5a + b+24=7b\), we get \(5a=6b - 24\), or \(a=\frac{6b - 24}{5}\).

Step3: Substitute \(a\) into the second equation

Substitute \(a=\frac{6b - 24}{5}\) into \(8b - 14=3b + a\).

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Step4: Find the value of \(a\)

Substitute \(b = 7\) into \(a=\frac{6b - 24}{5}\).

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Answer:

\(a = 3\), \(b = 7\)