Question

problem 3:
statement | reason

1. (gicong ki) | 1. given
2. (hi = ji) | 2. given
3. (angle gih=angle kij) | 3.
4. (\triangle gihcong\triangle kij) | 4.

problem 4:

Explanation:

Step1: Identify the congruence - related property

We are given two pairs of equal sides ($GI\cong KI$ and $HI = JI$) and a pair of equal angles ($\angle GIH=\angle KIJ$). The Side - Angle - Side (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: Determine the reason for triangle congruence

Since we have two pairs of equal sides and the included angles equal, we can conclude that $\triangle GIH\cong\triangle KIJ$ by the SAS congruence postulate.

Answer:

1. Vertical angles are congruent.
2. SAS (Side - Angle - Side) congruence postulate.