Question

question 5 of 5 select the correct answer from each drop - down menu. given: (overline{gh} cong overline{jh}) and (overline{ig} cong overline{ij}) prove: (\triangle ghi cong \triangle jhi) complete the proof. statements: (overline{gh} cong overline{jh}) and (overline{ig} cong overline{ij}); (overline{hi} cong overline{hi}); (\triangle ghi cong \triangle jhi) reasons: given; dropdown options: transitive property of congruence, commutative property of congruence, reflexive property of congruence; ... (diagram of a geometric figure with points g, i, j, h)

Explanation:

Step1: Analyze the congruent side

The side \( \overline{HI} \) is common to both \( \triangle GHI \) and \( \triangle JHI \). By the reflexive property of congruence, any segment is congruent to itself, so \( \overline{HI} \cong \overline{HI} \).

Step2: Identify the property

Among the given options (transitive, commutative, reflexive), the reflexive property of congruence states that a geometric figure is congruent to itself, which applies here for \( \overline{HI} \).

Answer:

reflexive property of congruence