Answer:
[tex]\textsf{D)}\quad \overline{TD} \cong \overline{SG}[/tex]
Step-by-step explanation:
If two triangles are congruent, their corresponding angles and sides are congruent.
In the context of congruent triangles, the order of the letters in the names of the congruent triangles are in the order of their corresponding vertices.
Therefore, given that ΔMTD ≅ ΔSLG, then the corresponding angles and sides are:
- ∠M ≅ ∠S
- ∠T ≅ ∠L
- ∠D ≅ ∠G
- MT ≅ SL
- TD ≅ LG
- MD ≅ SG
However, since none of these options are provided as answer choices, we can conclude that the naming of the triangles does not follow proper convention. Therefore, we have to determine congruency through observation of the diagram alone.
Upon closer inspection, it appears that triangle LSG is a reflection of triangle MTD across a vertical line. Therefore, ∠M ≅ ∠L, ∠T ≅ ∠S and ∠D ≅ ∠G. Similarly, MT ≅ LS, TD ≅ SG and MD ≅ LG.
So the statement that is true is:
[tex]\Large\boxed{\boxed{\overline{TD} \cong \overline{SG}}}[/tex]
