Question

1 multiple choice 1 point if triangle abc is congruent to triangle def, then which of the following is true?
\\(\overline{ab}\cong\overline{ef}\\)
\\(\angle b\cong\angle e\\)
\\(\angle a\cong\angle f\\)
\\(\overline{bc}\cong\overline{de}\\)

Explanation:

Step1: Recall congruent - triangle property

When $\triangle ABC\cong\triangle DEF$, corresponding parts are congruent. The order of the letters in the triangle names gives the correspondence: $A$ corresponds to $D$, $B$ corresponds to $E$, and $C$ corresponds to $F$.

Step2: Analyze each option

• $\overline{AB}$ corresponds to $\overline{DE}$, not $\overline{EF}$, so $\overline{AB}\cong\overline{EF}$ is false.
• $\angle B$ corresponds to $\angle E$, so $\angle B\cong\angle E$ is true.
• $\angle A$ corresponds to $\angle D$, not $\angle F$, so $\angle A\cong\angle F$ is false.
• $\overline{BC}$ corresponds to $\overline{EF}$, not $\overline{DE}$, so $\overline{BC}\cong\overline{DE}$ is false.

Answer:

B. $\angle B\cong\angle E$