Question

congruent triangles (topic 5)
what additional piece of information you would need in order to show that △efg≅△
o ∠f≅∠q
o ∠g≅∠p
o gf≅pq
o ∠e≅∠r

Explanation:

Step1: Recall congruence criteria

We know triangle - congruence criteria like SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), SSS (Side - Side - Side). Given one side is congruent (the marked sides), we need to match angles correctly.

Step2: Analyze angle - side relationships

For $\triangle EFG$ and $\triangle RPQ$, if we have $\angle G\cong\angle P$ and the included side between the angles at $G$ and $E$ in $\triangle EFG$ and the included side between the angles at $P$ and $R$ in $\triangle RPQ$ are already congruent (the marked sides), by the ASA (Angle - Side - Angle) congruence criterion, the two triangles will be congruent.

Answer:

$\angle G\cong\angle P$