Final answer:
To prove triangle congruence, use SSS if three pairs of corresponding sides are equal, SAS if two sides and the included angle are equal, HL for congruent hypotenuse and leg in right triangles, or ASA for two angles and the included side. Information given hints at similar triangles, requiring an understanding of AA similarity.
Step-by-step explanation:
To determine which property could be used to show that two triangles are congruent, it's essential to know the given information about the sides and angles of the triangles. The four properties used to prove triangles congruent are Side-Side-Side (SSS), Side-Angle-Side (SAS), Hypotenuse-Leg (HL), and Angle-Side-Angle (ASA). In the examples provided, it appears some triangles are similar, which means they have the same shape but not necessarily the same size. To prove congruency, which means triangles are identical in shape and size, one might take into account given lengths, shared sides, or angles as mentioned in the various scenarios.
If a scenario presents three pairs of equal corresponding sides, one might use SSS. If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, SAS could be used. The HL property is specific to right triangles and pertains to cases where the hypotenuse and one leg in one right triangle are congruent to the hypotenuse and a leg in another right triangle. Lastly, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the ASA property could be employed. Additionally, the phrase 'NO f A1 B1 AB' hinting at a sort of proportionality suggests a need for understanding similar triangles more than congruent ones, which might require a focus on properties such as AA (Angle-Angle) similarity postulate.