Answered

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a.loana established all necessary conditions but then used an inappropriate congruence cirterion
b.loana used a criterion that does not guarantee congruence
c.loana only established some of the necessary conditions for a congruence criterion
d.loana used an invalid reason to justify the Congruence of a pair of sides or angles
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Answer:

The correct option is

a. Loana established all necessary conditions but then used an inappropriate congruence criterion

Step-by-step explanation:

The two column proof is presented as follows;

Statement          [tex]{}[/tex]                    Reason

1. PQ = RQ = 9      [tex]{}[/tex]                  Given

2. m∠O = m∠S = 90° [tex]{}[/tex]             Given

3. m∠PQO = m∠RQS = 63° [tex]{}[/tex]   Given

4. ΔOPQ ≅ ΔSRQ [tex]{}[/tex]                  Angle-Side-Angle Congruence

The given parameters shows that the side, adjacent angle, and next adjacent angle of triangle ΔOPQ are congruent to the corresponding side, adjacent angle, and next adjacent angle of triangle ΔSRQ, therefore, the appropriate congruency criterion that shows that ΔOPQ is congruence to ΔSRQ [tex]{}[/tex]is the Side-Angle-Angle which is the same as the Angle-Angle-Side AAS, congruency criterion

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