Triangle mno is dilated to form new triangle pqr. if angle o is congruent to angle r, what other information will prove that the two triangles are similar? side on is congruent to side rq. angle n is congruent to angle q. side mn is congruent to side pq. angle m is congruent to angle q.

triangle mno is dilated to form a new triangle pqr. it is given that angle o is congruent to angle r. we need to find one condition to prove the triangles mno and pqr similar.

triangles are similar when they have the same shape, but not necessarily the same size. triangles can be proved similar by using many criteria as aa, sas, sss.

in this case, it is given that angle o is congruent to angle r.

we will apply aa criteria for similarity which states that

"if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar".

now, in triangles mno and pqr,

we will use the second option which says,

therefore, the triangles pqr and mno are similar by aa criteria.

so, option 2 is the correct answer.