Question

j is the midpoint of \overline{ik}, \triangle ghj is equilateral, and \overline{gk} \cong \overline{hi}. complete the proof that \triangle gjk \cong \triangle hji.

1 j is the midpoint of \overline{ik} given
2 \triangle ghj is equilateral given
3 \overline{gk} \cong \overline{hi} given
4 \overline{jk} \cong \overline{ij} definition of midpoint
5 \overline{gj} \cong \overline{hj} definition of equilateral triangle
6

Explanation:

Step1: Recall the SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the three pairs of congruent sides

We have \( \overline{GK}\cong\overline{HI}\) (given), \( \overline{JK}\cong\overline{JI}\) (definition of mid - point), and \( \overline{GJ}\cong\overline{HJ}\) (definition of equilateral triangle).

Answer:

Statement 6: \( \triangle GJK\cong\triangle HJI\)
Reason 6: SSS (Side - Side - Side) congruence criterion.