Question

question 6 (multiple choice worth 4 points) (02.03r mc) angle n = 40 degrees, side np = 8, angle q = 40 degrees, and side qs = 8. what additional information would you need to prove that δnop ≅ δqrs by asa? angle o is congruent to angle r. angle p is congruent to angle s. side no is congruent to side qr. side op is congruent to side rs.

Explanation:

Step1: Recall ASA congruence rule

ASA (Angle-Side-Angle) requires two consecutive angles of one triangle congruent to two consecutive angles of another triangle, with the included side between the angles congruent.

Step2: Map given congruent parts

We know $\angle N = 40^\circ = \angle Q$, and $NP = 8 = QS$. For $\triangle NOP \cong \triangle QRS$ by ASA, the side between the congruent angles must be congruent. For $\angle N$ and the next angle in $\triangle NOP$, the included side is $NO$; for $\angle Q$ and its corresponding next angle in $\triangle QRS$, the included side is $QR$.

Step3: Identify required congruence

Thus, we need $NO \cong QR$ to satisfy ASA.

Answer:

Side NO is congruent to side QR.