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Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

triangles EFG and YXZ in which triangle YXZ is larger than EFG

segment EF ~ segment XZ.
The measure of segment YZ is three times the size of segment EG.
segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX
There is a sequence of rigid motions that map ΔEFG onto ΔYXZ



Answer :

semsee45

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]

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