Question

step statement reason
1 fg = gi = 18 given
2 hg = gj = 11 given
3 ∠fgh ≅ ∠igj vertical angles are congruent
4 △fhg ≅ △ijg
show your work here
corresponding angles postulate aas congruence criterion
sas congruence criterion asa congruence criterion

Explanation:

Step1: Identify given side - length equalities

We are given that $FG = GI=18$ and $HG = GJ = 11$. These are two pairs of corresponding sides.

Step2: Identify the included - angle equality

We know that $\angle FGH\cong\angle IGJ$ because vertical angles are congruent. This angle is the included - angle between the pairs of corresponding sides.

Step3: Recall congruence criteria

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.

Step4: Determine the congruence of the triangles

Since we have two pairs of congruent sides ($FG\cong GI$ and $HG\cong GJ$) and the included angles $\angle FGH\cong\angle IGJ$, by the SAS congruence criterion, $\triangle FHG\cong\triangle IJG$.

Answer:

SAS Congruence Criterion