Question

is equilateral, \\( \angle i h j \cong \angle j g k \\), and \\( \overline { h i } \cong \overline { g k } \\).

statement
1 \\( \triangle g h j \\) is equilateral
2 \\( \angle i h j \cong \angle j g k \\)
3 \\( \overline { h i } \cong \overline { g k } \\)
4 \\( \overline { g j } \cong \overline { h j } \\)
5
reason
given
given
given
definition of equilateral triangle

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion 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.

Step2: Identify the triangles and their corresponding parts

We have \(\triangle JHI\) and \(\triangle JGK\). We know that \(\overline{HI}\cong\overline{GK}\) (given), \(\angle IHJ\cong\angle JGK\) (given), and \(\overline{GJ}\cong\overline{HJ}\) (from the definition of an equilateral triangle \(\triangle GHJ\)).

Step3: Apply the SAS congruence criterion

By the SAS congruence criterion, \(\triangle JHI\cong\triangle JGK\)

Answer:

\(\triangle JHI\cong\triangle JGK\) (by SAS congruence criterion)