Question

1. assume that δfgh ≅ δijh. which statements can be used to prove their congruence using the sss congruence postulate? select all that apply. ☐ gh ≅ jh ☐ gh ≅ ih ☐ fg ≅ ij ☐ fh ≅ ih

Explanation:

Answer:

To determine which statements prove \(\triangle FGH \cong \triangle IJH\) by SSS (Side - Side - Side) Congruence Postulate, we need to identify pairs of corresponding sides that are congruent. The SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

1. For the first option \(\overline{GH}\cong\overline{JH}\): This gives us a pair of corresponding sides.
2. For the second option \(\overline{GH}\cong\overline{JH}\) (it seems like a repeat, maybe a typo, but if we assume it's a valid side - pair).
3. For the third option \(\overline{FG}\cong\overline{IJ}\): This gives us another pair of corresponding sides.
4. For the fourth option \(\overline{FH}\cong\overline{IH}\): This gives us the third pair of corresponding sides.

If we have \(\overline{FG}\cong\overline{IJ}\), \(\overline{GH}\cong\overline{JH}\) and \(\overline{FH}\cong\overline{IH}\), then by SSS, \(\triangle FGH\cong\triangle IJH\).

So the statements that apply are \(\overline{GH}\cong\overline{JH}\), \(\overline{FG}\cong\overline{IJ}\) and \(\overline{FH}\cong\overline{IH}\) (assuming the second \(\overline{GH}\cong\overline{JH}\) is a valid representation of a side - pair and the other two as well). If we consider the check - box options:

• \(\overline{GH}\cong\overline{JH}\) (first and second check - boxes, assuming the second is a valid side - pair)
• \(\overline{FG}\cong\overline{IJ}\) (third check - box)
• \(\overline{FH}\cong\overline{IH}\) (fourth check - box)

So we would select the check - boxes corresponding to \(\overline{GH}\cong\overline{JH}\), \(\overline{FG}\cong\overline{IJ}\) and \(\overline{FH}\cong\overline{IH}\).