Question

j is the midpoint of \\( \overline{hi} \\). complete the proof that \\( \angle gji \cong \angle gjh \\).

Explanation:

Step1: Identify given statement

Given (J is midpoint of $\overline{HI}$)

Step2: Note marked congruent sides

Given (from diagram: $\overline{GH} \cong \overline{GI}$)

Step3: Use midpoint definition

Definition of midpoint ($\overline{HJ} \cong \overline{IJ}$)

Step4: Identify common side

Reflexive Property of Congruence ($\overline{GJ} \cong \overline{GJ}$)

Step5: Prove triangle congruence

SSS Congruence Postulate ($\triangle GHJ \cong \triangle GIJ$)

Step6: Corresponding parts congruent

CPCTC ($\angle GJI \cong \angle GJH$)

Answer:

1. Given
2. Given
3. Definition of midpoint
4. Reflexive Property of Congruence
5. SSS Congruence Postulate
6. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)