Question

Which of the following statements is true if m∠e = m∠y and m∠f = m∠x?

1) Triangles efg and yxz are congruent
2) Triangle yxz is larger than triangle efg
3) The measure of each segment in triangle yxz is three times the size of those in triangle efg
4) There is a sequence of rigid motions that map triangle efg onto triangle yxz

Answer 1

The statement that is true if the angles are congruent is option 4) There is a sequence of rigid motions that map triangle efg onto triangle yxz.

Step-by-step explanation:

The statement that is true if the angles are congruent is option 4) There is a sequence of rigid motions that map triangle efg onto triangle yxz.

Congruent angles in triangles indicate that the corresponding sides of the triangles are also congruent. This means that through a sequence of rigid motions, such as translations, rotations, and reflections, the two triangles can be superimposed on each other.

Options 1), 2), and 3) are not true because congruent angles do not necessarily imply congruent triangles, larger size, or proportional side lengths.