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 marked.
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 marked.
x =

Explanation:

Step1: Identify congruent sides

For triangles to be congruent by SSS, all three corresponding sides must be equal. From the diagrams, side \( BC \) in \( \triangle ABC \) corresponds to side \( EF \) (length 19) in \( \triangle DEF \), and \( AC \) corresponds to \( DF \), \( AB \) corresponds to \( DE \). So, \( BC = EF \).

Step2: Set up equation

Given \( BC = x - 4 \) and \( EF = 19 \), set \( x - 4 = 19 \).

Step3: Solve for x

Add 4 to both sides: \( x = 19 + 4 = 23 \).

Answer:

\( x = 23 \)