Question

1. using the transitive property of congruence, if (overline{cd} cong overline{ef}) and (overline{ef} cong overline{gh}), then ______ (overline{cd} cong overline{ef}). (overline{ef} cong overline{gh}). (overline{cd} cong overline{gh}). (overline{ef} cong overline{ef}).

Explanation:

Step1: Recall Transitive Property

The Transitive Property of Congruence states that if \( a \cong b \) and \( b \cong c \), then \( a \cong c \).

Step2: Apply to Given Segments

Here, \( \overline{CD} \cong \overline{EF} \) (so \( a = \overline{CD} \), \( b = \overline{EF} \)) and \( \overline{EF} \cong \overline{GH} \) (so \( c = \overline{GH} \)). By transitive property, \( \overline{CD} \cong \overline{GH} \).

Answer:

\( \boldsymbol{\overline{CD} \cong \overline{GH}} \) (corresponding option: the one with \( \overline{CD} \cong \overline{GH} \))