Question

from unit 2. lesson 2
triangle hef is the image of triangle hgf after a reflection across line fh.

write a congruence statement for the two congruent triangles.

from unit 2. lesson 3
triangle abc is congruent to triangle edf. so lin knows that there is a sequence of rigid motions that takes abc to edf.

select all true statements after the transformations.
a angle a coincides with angle f.
b angle b coincides with angle d.
c angle c coincides with angle e.
d segment ba coincides with segment de.
e segment bc coincides with segment fe.

Explanation:

Step1: Analyze triangle congruence

Since \(\triangle ABC\cong\triangle EDF\), corresponding parts are congruent.
For angles: \(\angle A\) corresponds to \(\angle F\), \(\angle B\) corresponds to \(\angle D\), \(\angle C\) corresponds to \(\angle E\).
For sides: \(BA\) corresponds to \(FD\), \(BC\) corresponds to \(DE\), \(AC\) corresponds to \(EF\).

Step2: Check each option

• Option A: \(\angle A\) corresponds to \(\angle F\), so this is true.
• Option B: \(\angle B\) corresponds to \(\angle D\), so this is true.
• Option C: \(\angle C\) corresponds to \(\angle E\), so this is true.
• Option D: \(BA\) corresponds to \(FD\), not \(DE\), so this is false.
• Option E: \(BC\) corresponds to \(DE\), not \(FE\), so this is false.

Answer:

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