Answer:
[tex]\textsf{C)}\quad \dfrac{\overline{EF}}{\overline{YX}}=\dfrac{\overline{EG}}{\overline{YZ}}=\dfrac{\overline{GF}}{\overline{ZX}}[/tex]
Step-by-step explanation:
AA similarity (Angle-Angle similarity) states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Given that m∠E = m∠Y and m∠F = m∠X in triangles EFG and YXZ, then the triangles are similar by AA similarity.
In similar triangles, corresponding sides are always in the same ratio.
In this case, angle E corresponds to angle Y, angle F corresponds to angle X, and angle G corresponds to angle Z. Therefore:
[tex]\dfrac{\overline{EF}}{\overline{YX}}=\dfrac{\overline{EG}}{\overline{YZ}}=\dfrac{\overline{GF}}{\overline{ZX}}[/tex]
