Answer:
Question 1: We need to know whether Angles P and N are congruent or not.
Question 2: Cannot be proven congruent
Question 3: AAS Congruence Theorem
Question 4: ASA Congruence Postulate
Step-by-step explanation:
Background info: The information (congruence lines on sides and angles) is read counterclockwise (starting from the very left to right).
Question 1: In order to prove the triangles congruent with the AAS, we need two pairs of congruent angles and one pair of congruent sides. We still need one more pair of congruent angles. Since the triangle is read counterclockwise, the angle to the left of the current congruent angle given needs to be given to us. This is angles P and N.
Question 2: For this answer, the triangles cannot be proven congruent because we are only given three congruent angle pairs. This means that it should be the "AAA" Theorem, however, it doesn's exist due to the fact that the triangles could still be two different sizes despite the fact that the angles are the same. In order to prove this congruent, we would need info on congruent sides.
Question 3: Reading the triangle left to right, we see a congruent angle pair (A), another congruent angle pair (A), and a congruent side pair (S). Putting this together, we get AAS.
Question 4: Reading the triangle left to right, we see an angle pair (A), a side pair (S), and an angle pair (A). Putting this together, we get ASA.
Hope this helps! (No guarantees it's 100% correct)
