Question

multiple choice 1 point what additional information do you need to prove the triangles are congruent by sas? options: mn ≅ qn, lm ≅ qp, ∠m ≅ ∠q, ∠p ≅ ∠l, clear my selection

Explanation:

Step1: Identify given info

Vertical angles $\angle MNL = \angle PNQ$; $MN = PN$, $LN = QN$ (marked congruent).

Step2: Check SAS requirements

SAS needs two sides + included angle. Given sides: $MN=PN$, $LN=QN$. Included angles: $\angle MNL$ (between $MN,LN$) and $\angle PNQ$ (between $PN,QN$) are vertical angles (congruent). All SAS conditions met.

Step3: Evaluate options

No additional info is needed as existing marked congruences and vertical angles satisfy SAS.

Answer:

No additional information is needed (assuming the option for no extra info is implied, but based on typical congruence proofs with marked sides/vertical angles, SAS is already satisfied).

Wait, correcting: The problem asks for "additional information"—but with $MN\cong PN$, $LN\cong QN$, and $\angle MNL\cong\angle PNQ$ (vertical angles), SAS is already proven. So no additional info is required. But if the options include a "none" choice, that's the answer. Since the user's image options might have that, but based on standard proof: