Question

question 4
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 by the aa similarity postulate?
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 o

Explanation:

Step1: Recall AA similarity postulate

AA (Angle - Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Step2: Analyze given information

We know that \(\angle O\cong\angle R\). We need one more pair of congruent angles.

• Option 1: Side \(ON\) is congruent to side \(RQ\). This is a side - side condition, not relevant for AA similarity.
• Option 2: \(\angle N\cong\angle Q\). Now we have two pairs of congruent angles (\(\angle O\cong\angle R\) and \(\angle N\cong\angle Q\)), which satisfies AA similarity postulate.
• Option 3: Side \(MN\) is congruent to side \(PQ\). This is a side - side condition, not relevant for AA similarity.
• Option 4: \(\angle M\cong\angle O\). This gives only one new angle congruence (but we already have \(\angle O\) related to \(\angle R\)), not a second pair for the two different triangles.

Answer:

Angle \(N\) is congruent to angle \(Q\)