Question

which explains whether ∠vgh is congruent to ∠vjh? they are congruent because gh ≅ gv, jf ≅ jh, and fh ≅ vh. they are congruent because opposite sides of a parallelogram are congruent. they are not congruent because only one pair of corresponding sides is congruent. they are not congruent because only two pairs of corresponding sides are congruent.

Explanation:

Step1: Recall SSS Congruence Criterion

The SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
In \(\triangle FGH\) and \(\triangle VJH\), we have \(GH\cong GV\) (given), \(JF\cong JH\) (given), and \(FH\cong VH\) (common side).

Step2: Apply SSS Criterion

Since \(GH\cong GV\), \(JF\cong JH\), and \(FH\cong VH\), by the SSS congruence criterion, \(\triangle FGH\cong\triangle VJH\).
If two triangles are congruent, then their corresponding angles are congruent. So, \(\angle FGH\cong\angle VJH\)

Answer:

They are congruent because \(GH\cong GV\), \(JF\cong JH\), and \(FH\cong VH\)