Question

assume $\triangle abc \cong \triangle def$. if $ab = 12$, $bc = 15$, and partially obscured value 17, what is the length of $\overline{ef}$?
a. 17
b. 10
c. 15
d. cannot be determined

Explanation:

Step1: Recall Congruent Triangles

Congruent triangles have corresponding sides equal. So, in \( \triangle ABC \cong \triangle DEF \), the order of the letters matters. This means \( AB \) corresponds to \( DE \), \( BC \) corresponds to \( EF \), and \( AC \) corresponds to \( DF \).

Step2: Identify Corresponding Side

We need to find the length of \( \overline{EF} \). From the correspondence, \( BC \) (in \( \triangle ABC \)) corresponds to \( EF \) (in \( \triangle DEF \)). We know \( BC = 15 \), so by the property of congruent triangles, \( EF = BC \).

Step3: Determine Length of \( EF \)

Since \( BC = 15 \), then \( EF = 15 \).

Answer:

C. 15