Correct me PLS!

Question

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

 m∠E > m∠Z 

ΔEFG ~ ΔYXZ 

The measure of each segment in ΔYXZ is three times the size of those in ΔEFG. 

There is a sequence of rigid motions that map ΔEFG onto ΔYXZ.

WOULD IT BE OPTION 2, correct me and pls just give me the answer and steps on this practice problem.

Answer 1

If the m∠E = m∠Y and if the m∠F = m∠X, then ∠E ≅ ∠Y and ∠F ≅ ∠X. Then by the Angle-Angle (AA) Similarity Postulate the two triangles are similar. You write the similarity statement like this:

making sure the congruent angles of the first triangle line up with the congruent angles of the second triangle.

Please note that if two pairs of angles are congruent, then the last pair MUST be congruent because there are 180° in every triangle.