Question

1. identify the missing information from the 2 - column proof.

diagram: two triangles (igh and edf) with sides of length 5, 11, and 113° angles at g and d. statements: $overline{hg} \cong \overline{ed}$ (given), $overline{gi} \cong \overline{df}$ (given), missing statement, $\triangle hgi \cong \triangle edf$ (sas congruence postulate). reasons: given, given, ?, sas. options: $overline{ih} \cong \overline{fe}$, $overline{gi} \cong \overline{fd}$, $\angle g \cong \angle d$, $\angle h \cong \angle e$

Explanation:

Step1: Recall SAS Congruence

SAS requires two sides and included angle. Given \( \overline{HG} \cong \overline{ED} \), \( \overline{GI} \cong \overline{DF} \), need included angle \( \angle G \cong \angle D \) (both \( 113^\circ \)).

Step2: Analyze Options

• \( \overline{IH} \cong \overline{FE} \): Not needed for SAS.
• \( \overline{GI} \cong \overline{FD} \): Already given.
• \( \angle G \cong \angle D \): Matches included angle for SAS.
• \( \angle H \cong \angle E \): Result of congruence, not a given for SAS.

Answer:

\( \angle G \cong \angle D \) (the option with \( \angle G \cong \angle D \))