Question

triangle abc is congruent to triangle edf. so, priya knows that there is a sequence of rigid motions that takes abc to edf. select all true statements after the transformations: (lesson 2 - 3) a. segment ab coincides with segment ef. b. segment bc coincides with segment df. c. segment ac coincides with segment ed. d. angle a coincides with angle e. e. angle c coincides with angle f.

Explanation:

Step1: Recall congruent - triangle property

When $\triangle ABC\cong\triangle EDF$, corresponding sides and angles are equal. The order of the letters in the triangle - congruence statement indicates the correspondences. That is, $A$ corresponds to $E$, $B$ corresponds to $D$, and $C$ corresponds to $F$.

Step2: Check side - correspondences

For sides, $AB$ corresponds to $ED$, $BC$ corresponds to $DF$, and $AC$ corresponds to $EF$.

Step3: Check angle - correspondences

For angles, $\angle A$ corresponds to $\angle E$, $\angle B$ corresponds to $\angle D$, and $\angle C$ corresponds to $\angle F$.

Answer:

B. Segment $BC$ coincides with segment $DF$.
D. Angle $A$ coincides with angle $E$.
E. Angle $C$ coincides with angle $F$.