Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). if δabc and δgef are congruent, the value of x is
and the value of y is

Explanation:

Step1: Identify congruent sides

Since \(\triangle ABC \cong \triangle EGF\) (assuming the correct correspondence, likely \(AB = EG\), \(BC = GF\), \(AC = EF\)). From the diagram, \(BC = 4\), \(AC = 2\), \(GF = x - 8\), \(EF = x - y\). Also, \(AB\) and \(EG\) should be equal, but let's focus on \(BC\) and \(GF\) first. So \(BC = GF\), so \(4 = x - 8\).

Step2: Solve for \(x\)

Solve \(x - 8 = 4\). Add 8 to both sides: \(x = 4 + 8 = 12\).

Step3: Solve for \(y\)

Now, \(AC = EF\), so \(2 = x - y\). We know \(x = 12\), so substitute: \(2 = 12 - y\). Subtract 12 from both sides: \(-10 = -y\), so \(y = 10\).

Answer:

The value of \(x\) is \(12\) and the value of \(y\) is \(10\).