Question

1. in the figure below, δdgf ≅ δdef. which statement cannot be used to prove the congruence of the triangles using the sss congruence postulate? given gf ≅ ef; given eh ≅ gh; given de ≅ dg; reflexive property df ≅ df

Explanation:

To prove \(\triangle DGF \cong \triangle DEF\) using SSS (Side - Side - Side) Congruence Postulate, we need to show that all three corresponding sides of the two triangles are equal.

• For the option "Given \(GF = EF\)": We can see from the figure that \(EF = 12\) in and \(GF=12\) in, so this can be used to show a pair of corresponding sides are equal.
• For the option "Given \(EH = GH\)": \(EH\) and \(GH\) are segments related to the diagonals of the quadrilateral, not the sides of \(\triangle DGF\) and \(\triangle DEF\). So this statement cannot be used to prove the congruence of the two triangles using SSS.
• For the option "Given \(DE = DG\)": We can see from the figure that \(DE = 4\) in and \(DG = 4\) in, so this can be used to show a pair of corresponding sides are equal.
• For the option "Reflexive Property \(DF=DF\)": By the reflexive property of congruence, a side is congruent to itself. So \(DF\) is a common side to both \(\triangle DGF\) and \(\triangle DEF\), and this can be used in the SSS proof.

Answer:

Given \(EH = GH\)