Question

1. triangle abc is congruent to triangle def. select all the statements that are a result of corresponding parts of congruent triangles being congruent. (lesson 2 - 1) a segment ac is congruent to segment ef. b segment bc is congruent to segment ef. c angle bac is congruent to angle edf. d angle bca is congruent to angle edf. e angle cba is congruent to angle fed.

Explanation:

Step1: Recall congruent - triangles property

When \(\triangle ABC\cong\triangle DEF\), corresponding sides and corresponding angles 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: Check side - congruence

For sides, \(AB\) corresponds to \(DE\), \(BC\) corresponds to \(EF\), and \(AC\) corresponds to \(DF\). So, segment \(BC\) is congruent to segment \(EF\) (Option B is correct), and segment \(AC\) is not congruent to segment \(EF\) (Option A is incorrect).

Step3: Check angle - congruence

For angles, \(\angle BAC\) corresponds to \(\angle EDF\) (Option C is correct), \(\angle BCA\) corresponds to \(\angle EFD\) (Option D is incorrect), and \(\angle CBA\) corresponds to \(\angle FED\) (Option E is correct).

Answer:

B. Segment \(BC\) is congruent to segment \(EF\).
C. Angle \(BAC\) is congruent to angle \(EDF\).
E. Angle \(CBA\) is congruent to angle \(FED\).