Question

complete the proof that \\( \angle h \cong \angle i \\).

Explanation:

Step1: Recall the Side - Angle - Side (SAS) Congruence Postulate

The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle FIJ\) and \(\triangle GHJ\), we have \(\overline{GJ}\cong\overline{FJ}\) (given), \(\overline{IJ}\cong\overline{HJ}\) (given), and \(\angle FIJ\cong\angle GJH\) (Vertical Angle Theorem).

Step2: Apply the SAS Congruence Postulate

Since we have two sides and the included angle of \(\triangle FIJ\) congruent to two sides and the included angle of \(\triangle GHJ\), by the Side - Angle - Side (SAS) Congruence Postulate, \(\triangle FIJ\cong\triangle GHJ\).

Answer:

SAS (Side - Angle - Side) Congruence Postulate.