Question

what value of x will make the triangles congruent by sss?
triangle abc with side bc labeled (x - 4), side ab with one tick mark, side ac with two tick marks, and angle at a. triangle def (labeled d, e, f) with side de with one tick mark, side df with two tick marks, side ef labeled 19, and angle at d.
x = \boxed{}

Explanation:

Step1: Identify congruent sides

For SSS congruence, all three sides must be equal. From the diagrams, side \( BC \) in \( \triangle ABC \) and side \( EF \) (length 19) in \( \triangle DEF \) should be equal when triangles are congruent. So \( x - 4 = 19 \).

Step2: Solve for \( x \)

Add 4 to both sides of the equation \( x - 4 = 19 \): \( x = 19 + 4 \).

Answer:

\( x = 23 \)