Answer:
(a) PQR by ASA
(b) MNO by SSS
(c) STU by SAS
Step-by-step explanation:
You want to know the congruence postulates that can be invoked to show ∆XYZ is congruent to each of ∆PQR, ∆MNO, ∆STU.
∆XYZ
All of the sides and angles are marked in ∆XYZ, so congruence with another triangle will depend on what sides and/or angles are marked in that triangle.
(a) ∆PQR
Angle P, side PQ, and angle Q are marked in ∆PQR, so we can claim congruence with ∆XYZ by ASA.
(b) ∆MNO
Side MN, side NO, and side OM are marked in ∆MNO, so we can claim congruence with ∆XYZ by SSS.
(c) ∆STU
Side SU, angle S, and side ST are marked in ∆STU, so we can claim congruence with ∆XYZ by SAS.
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Additional comment
In the congruence postulate abbreviations, S represents corresponding sides, and A represents corresponding angles. The order of A and S reflects the order of the corresponding angles/sides in the respective triangles.
That is, the markings would differ in triangles congruent by AAS or ASA, even though two angles and a side are congruent in both cases. In the latter case, the corresponding marked sides are between the corresponding marked angles. In the former case, they are not.
In ∆XYZ, the vertices in order are the right angle, the angle marked with a single arc, and the angle marked with a double arc. The side markings are a double mark for XY, a triple mark for YZ, and a single mark for ZX. In claiming congruence to the other triangles, we need to check that corresponding parts are similarly marked. (They are.)
