Given:
A diagram of two triangles.
To find:
Whether the triangles are congruent or not.
Solution:
In triangles DEF and DGF,
[tex]m\angle EDF\cong m\angle GDF[/tex] (Given)
[tex]\overline{DF}\cong \overline{DF}[/tex] (Reflexive property)
[tex]m\angle DFE\cong m\angle DFG[/tex] (Given)
Two corresponding angles and their included angles are congruent, so the triangles are congruent by ASA postulate.
[tex]\Delta DE F\cong \Delta DGF[/tex] (ASA congruence postulate)
Therefore, yes the triangles are congruent by ASA. Hence the correct option is A.
