Question

12.question anSwer pls accurate

Answer 1

Consider the two triangles OPQ and ORS.

PQ=RS (Given)

Angle PQO = Angle RSO = 90°

Angle POQ = Angle ROS. (vertically opposite angles)

By AAS Congruence we have ,

Triangle OPQ is congruent to Triangle ORS.

OQ=OS......(BY CPCT)

This implies that PR and QS bisect each other.

Hence proved.

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Answer 2

From the given statement, we must consider PQRS as a straight line, where P, Q, R and S are followed by one another.

                            PQ = RS from the diagram.

                   PQ + QR = QR + RS ( by using addition postulate)

                   PQ + QR = PR (segment addition, betweeness)

                    QR + RS = QS (segment addition, betweeness)

Therefore, the segment PR must be equal to QS.

Hence proved.