Question

1. triangle abc is congruent to triangle edf. so, mai 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. angle a coincides with angle e. b. angle b coincides with angle f. c. segment ab coincides with segment ef. d. segment bc coincides with segment df. e. segment ac coincides with segment ed.

Explanation:

Step1: Recall congruent - triangle property

When $\triangle ABC\cong\triangle EDF$, corresponding angles and sides are equal. The order of the vertices in the congruence statement gives the corresponding parts. That is, $\angle A$ corresponds to $\angle E$, $\angle B$ corresponds to $\angle D$, $\angle C$ corresponds to $\angle F$, $AB$ corresponds to $ED$, $BC$ corresponds to $DF$, and $AC$ corresponds to $EF$.

Step2: Check each option

• Option A: $\angle A$ corresponds to $\angle E$, so angle $A$ coincides with angle $E$. This is true.
• Option B: $\angle B$ corresponds to $\angle D$, not $\angle F$. So this is false.
• Option C: $AB$ corresponds to $ED$, not $EF$. So this is false.
• Option D: $BC$ corresponds to $DF$, so segment $BC$ coincides with segment $DF$. This is true.
• Option E: $AC$ corresponds to $EF$, not $ED$. So this is false.

Answer:

A. Angle A coincides with angle E.
D. Segment BC coincides with segment DF.