91影视

Since, first and second statement of two column proof are given in the question. So, there reason must be 鈥淕iven鈥�.

Since, midpoint is a point on a line segment that divides it into two congruent line segments

Thus,$O$ divides line segment$\stackrel{炉}{PS}$in two congruent line segments

Hence, reason of third statement must be

鈥淎蝉$O$ is the midpoint of$\stackrel{炉}{PS}$ and midpoint is a point on a line segment that divides it into two congruent line segments鈥�

Observe from figure,$鈭�POQ$and$鈭�SOR$ are vertically opposite angles and such angles are congruent

So reason for$鈭�POQ鈮�鈭�SOR$ will be 鈥淰ertically opposite angles鈥�

According to ASA congruence criteria, two triangles are said to be congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle

Using statement 1, 3, and 4 $螖POQ鈮�螖SOR$

So its reason will be 鈥淎SA Congruence Criteria鈥�

Since, corresponding parts of congruent triangles are equal

So, $\stackrel{炉}{QO}鈮�\stackrel{炉}{RO}$because of same reason

As$\stackrel{炉}{QO}鈮�\stackrel{炉}{RO}$and midpoint is a point on a line segment that divides it into two congruent line segments

Thus, it the reason for the statement 鈥�$O$is the midpoint of $\stackrel{炉}{RQ}$鈥�

Hence, complete proof will be