Question

type the correct answer in each box. spell all words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s).

△abc and △fde are congruent by the criterion. (use the three - letter abbreviation without spaces )
the value of x is, and the value of y is.

Explanation:

Step1: Identify congruence criterion

Since \(AB = DF = 3\), \(BC = DE = 14\), \(AC = FE\) (marked as equal), by SSS (Side - Side - Side) criterion \(\triangle ABC\cong\triangle FDE\).

Step2: Solve for \(x\)

We know that \(BC=x + 3\) and \(DE = 14\). Since \(BC=DE\) (congruent triangles have equal corresponding sides), we have the equation \(x+3=14\).
Subtract 3 from both sides: \(x=14 - 3=11\).

Step3: Solve for \(y\)

We know that \(AB=x - y\) and \(AB = 3\), \(x = 11\). Substitute \(x = 11\) into the equation \(x-y=3\).
We get \(11-y=3\). Add \(y\) to both sides: \(11=3 + y\). Then subtract 3 from both sides: \(y=11 - 3=8\).

Answer:

SSS; \(11\); \(8\)