Question

from unit 2, lesson 3
triangle abc is congruent to triangle fde. so lin knows that there is a sequence of rigid
motions that takes abc to fde.
select all true statements after the transformations.
angle a coincides with angle f.
angle b coincides with angle d.
angle c coincides with angle e.
segment ba coincides with segment de.
segment bc coincides with segment fe.

Explanation:

Step1: Recall congruent triangle properties

Congruent triangles have corresponding angles and sides equal. If \(\triangle ABC\cong\triangle FDE\), then \(\angle A=\angle F\), \(\angle B = \angle D\), \(\angle C=\angle E\), \(BA = FD\), \(BC=DE\), \(AC = FE\).

Step2: Analyze each option

• Option A: Since \(\angle A=\angle F\), angle \(A\) coincides with angle \(F\).
• Option B: Since \(\angle B=\angle D\), angle \(B\) coincides with angle \(D\).
• Option C: Since \(\angle C=\angle E\), angle \(C\) coincides with angle \(E\).
• Option D: \(BA\) corresponds to \(FD\), not \(DE\).
• Option E: \(BC\) corresponds to \(DE\), not \(FE\).

Answer:

A. Angle \(A\) coincides with angle \(F\), B. Angle \(B\) coincides with angle \(D\), C. Angle \(C\) coincides with angle \(E\)