Question

Triangle D E F is reflected across D F to form triangle E G F. The lengths of sides E F and F G are congruent.

To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed?

∠DEF ≅ ∠ DGF
∠DFE ≅ ∠ DFG
DE ≅ DG
DG ≅ GF

Answer 1

(b) ∠DFE ≅ ∠DFG

Explanation:

You want to know what additional information is required to show ∆DEF ≅ ∆DGF by SAS, given FE≅FG.

SAS

The SAS congruence postulate requires pairs of corresponding sides be congruent, along with the angle between those sides.

We know that FD is congruent to itself, and we are given FE≅FG. The angles between these sides are ∠DFE and ∠DFG.

To make use of the SAS congruence postulate, we need to know that ...

∠DFE ≅ ∠DFG, choice B

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