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

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                              Reason

1. PQ = RQ = 9                        Given

2. m∠O = m∠S = 90°             Given

3. m∠PQO = m∠RQS = 63°   Given

4. ΔOPQ ≅ ΔSRQ                  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 is the Side-Angle-Angle which is the same as the Angle-Angle-Side AAS, congruency criterion

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.