Question

question 4
10 pts
g.gsr.3.4 (mc)
what can we prove to be true using the reflexive property for this diagram?
diagram of a triangle with points a, b, c, d, e, f
options:

• $\underline{fa} \cong \underline{fc}$
• $\angle bae \cong \angle bcd$
• $\angle abc \cong \angle cba$
• $\underline{ab} \cong \underline{cb}$

Explanation:

The reflexive property states that a geometric figure (angle, segment, etc.) is congruent to itself. Let's analyze each option:

• Option 1: \( \overline{FA} \cong \overline{FC} \) – This would require some other property (like triangle congruence or midpoint), not reflexive.
• Option 2: \( \angle BAE \cong \angle BCD \) – These are different angles, not the same angle, so reflexive doesn't apply.
• Option 3: \( \angle ABC \cong \angle CBA \) – \( \angle ABC \) and \( \angle CBA \) are the same angle (just named in reverse order), so by the reflexive property, an angle is congruent to itself.
• Option 4: \( \overline{AB} \cong \overline{CB} \) – There's no indication \( AB = CB \) from the diagram or reflexive property (reflexive is about a figure being congruent to itself, not two different segments).

Answer:

C. \( \angle ABC \cong \angle CBA \)