NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.4

Question 4

Step 1: We are given that \(PQRS\) is a parallelogram. So, opposite sides are parallel. That means \(PQ \parallel SR\) and \(PS \parallel QR\).

Step 2: It is also given that \(AB \parallel PS\). Since \(PS \parallel QR\), we can say: \(AB \parallel QR\).

Step 3: Look at diagonal \(PR\). It cuts the parallelogram into two triangles: - \(\triangle APS\) on the left, - \(\triangle PQR\) on the right.

Step 4: In \(\triangle PQR\), line \(AB\) is drawn parallel to \(QR\). From the Basic Proportionality Theorem (Thales’ theorem), we know this will divide the sides proportionally.

Step 5: By that property, we can say the triangles formed are similar: \(\triangle OAB \sim \triangle OPS\) (AA similarity, because corresponding angles are equal when lines are parallel).

Step 6: From similarity, corresponding sides are parallel. That gives \(OC \parallel SR\).

Step 7: Therefore, we have proved that \(OC \parallel SR\).

Final Answer: \(OC \parallel SR\).