Question

1. asa
2. asa
3. sss
4. sss
5. sas

18)
19)

1. np

Explanation:

Step1: Analyze Problem 13 (ASA)

Check if two angles and the included side are congruent. The triangles have vertical angles (equal) and marked congruent sides/angles matching ASA. So ASA applies.

Step2: Analyze Problem 14 (ASA)

Identify angles and included side. Vertical angles and marked congruent parts fit ASA criteria. So ASA is correct.

Step3: Analyze Problem 15 (SSS)

Check all three sides. Marked tick marks show three pairs of congruent sides, so SSS (Side - Side - Side) congruence applies.

Step4: Analyze Problem 16 (SSS)

Three pairs of sides with tick marks, so SSS congruence is valid.

Step5: Analyze Problem 17 (SAS)

Two sides and included angle: marked sides and vertical angle (included) are congruent, so SAS (Side - Angle - Side) works.

Step6: Analyze Problem 18 (ASA or SAS? Wait, marked side and right angle. Wait, the diagram has a right angle and marked sides. Wait, actually, the triangles share a side, and two sides are marked. Wait, no, looking at the diagram, it's SAS? Wait, no, the original mark: the triangles are formed by a median? Wait, no, the tick marks: two sides and included angle? Wait, no, the problem 18: the triangles have a common side, and two other sides marked. Wait, actually, the right angle and two sides: so SAS (since right angle is included between two sides). Wait, but the label? Wait, the user's diagram: problem 18 has a right angle, marked sides. So SAS? Wait, no, maybe ASA? Wait, no, the key is to check the congruence criteria.

Wait, maybe I misread. Let's re - check:

Problem 13: ASA (two angles, included side)
Problem 14: ASA (two angles, included side)
Problem 15: SSS (three sides)
Problem 16: SSS (three sides)
Problem 17: SAS (two sides, included angle)
Problem 18: Let's see, the triangles have a right angle, a common side, and one other side marked. So SAS (right angle is included between the common side and the marked side).
Problem 19: Let's check. One side marked, two angles. Wait, the first triangle has a side and two angles, the second has a side and two angles. Wait, is it AAS? But the label? Wait, the user's diagram: problem 19 has a side marked and two angles. Wait, maybe ASA? No, AAS. But the original label? Wait, the user's diagram: problem 19 is labeled? Wait, no, the user's image: problem 19 has two triangles, one with a side marked and two angles, the other with a side marked and two angles. Maybe AAS, but the given label? Wait, the user's problem: maybe we are to confirm the congruence criteria.
Problem 20: NP (Not Possible) because the angles and sides don't match congruence criteria.

But since the question is about identifying the congruence criteria (maybe confirming the labels), let's take problem 15 as an example. For problem 15, we have three sides with tick marks (one side with three ticks, one with two, one with one), so SSS is correct.

Answer:

For example, in problem 15, the congruence criterion is SSS (Side - Side - Side) as all three pairs of corresponding sides are congruent (marked by tick marks). (If we take problem 13, the answer is ASA (Angle - Side - Angle) as two angles and the included side are congruent.)