Question

In Fig., ∠POQ ≅ ∠ROS, can we say that ∠POR ≅ ∠QOS

Answer 1

We have,

$$\begin{gathered} \text{∠POQ ≅∠ROS (1)} \\ \text{Also, ∠ROQ ≅∠ROQ (same angle)} \\ \text{Therefore, adding ∠ROQ to both sides of (1), we get:} \\ \text{∠POQ +∠ROQ ≅∠ROQ +∠ROS} \\ \text{Therefore, ∠POR ≅ ∠QOS} \\ \text{Hence proved.} \end{gathered}$$