Complete the two-column proof for the following theorem. Given: angle P Q S and angle R Q S are right angles. Prove: angle P Q S cong angle R Q S What reason fits 2? 2 choose your answer... 1. Given 2. square 3. Definition of right angles 4. Substitution Property 5. angle P Q S=angle R Q S

To complete the two-column proof for the given theorem, we need to fill in the missing reasons that logically lead from the given information to the conclusion that \(\angle PQS \cong \angle RQS\).Step 1: The first statement is given, which is that \(\angle PQS\) and \(\angle RQS\) are right angles. The reason for this statement is "Given."Step 2: The second statement is that the measure of \(\angle PQS\) is 90 degrees. The reason for this statement is the "Definition of right angles," which states that a right angle is an angle with a measure of 90 degrees.Step 3: The third statement should be that the measure of \(\angle RQS\) is also 90 degrees. This is because \(\angle RQS\) is also a right angle, as given in the first statement. The reason for this statement is the same as for the second statement, which is the "Definition of right angles."Step 4: The fourth statement is that \(\angle PQS\) is congruent to \(\angle RQS\). To reach this conclusion, we use the fact that both angles have the same measure, which is 90 degrees. The reason for this statement is the "Substitution Property," which allows us to substitute equal quantities for each other.Step 5: The fifth statement is the conclusion that \(\angle PQS \cong \angle RQS\). The reason for this statement is the "Definition of Congruent Angles," which states that angles are congruent if they have the same measure.Here is the completed proof:\begin{array}{l|l}\multicolumn{1}{c|}{\ Statements\ }\ &\ \multicolumn{1}{c}{\ Reasons\ }\ \\\hline\ 1.\ \angle\ PQS\ and\ \angle\ RQS\ are\ right\ angles\ &\ 1.\ Given\ \\2.\ m\angle\ PQS\ =\ 90^\circ\ &\ 2.\ Definition\ of\ right\ angles\ \\3.\ m\angle\ RQS\ =\ 90^\circ\ &\ 3.\ Definition\ of\ right\ angles\ \\4.\ m\angle\ PQS\ =\ m\angle\ RQS\ &\ 4.\ Substitution\ Property\ \\5.\ \angle\ PQS\ \cong\ \angle\ RQS\ &\ 5.\ Definition\ of\ Congruent\ Angles\ \\\end{array}Answer: The reason that fits statement 2 is the "Definition of right angles."