Question

1. 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).

$\triangle abc$ and $\triangle fde$ are congruent by the $\boldsymbol{square}$ criterion. (use the three-letter abbreviation without spaces.)
the value of $x$ is $\boldsymbol{square}$ , and the value of $y$ is $\boldsymbol{square}$.

Explanation:

Step1: Match congruent sides

$\overline{BC} = \overline{ED} \implies x+3 = 14$

Step2: Solve for x

$x = 14 - 3 = 11$

Step3: Match another pair of sides

$\overline{AB} = \overline{FD} \implies 3 = x-y$

Step4: Substitute x, solve for y

$3 = 11 - y \implies y = 11 - 3 = 8$

Step5: Identify congruence criterion

All three pairs of corresponding sides are congruent, so the criterion is SSS.

Answer:

The value of x is 11, and the value of y is 8.
$\Delta ABC$ and $\Delta FDE$ are congruent by the SSS criterion.