Question

1. what values of x and y make (\triangle pqrcong\triangle jih)?

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle PQR\cong\triangle JIH\), their corresponding sides are equal. So, \(y + 12=5y\) and \(10x=x + 36\).

Step2: Solve the equation for \(x\)

For \(10x=x + 36\), subtract \(x\) from both sides: \(10x-x=x + 36-x\), which gives \(9x=36\). Then divide both sides by \(9\): \(x=\frac{36}{9}=4\).

Step3: Solve the equation for \(y\)

For \(y + 12=5y\), subtract \(y\) from both sides: \(y+12 - y=5y - y\), which gives \(12 = 4y\). Then divide both sides by \(4\): \(y=\frac{12}{4}=3\).

Answer:

\(x = 4\), \(y=3\)