Ex.6.3 Q5 Triangles Solution - NCERT Maths Class 10

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Question

\(S\) and \(T\) are points on sides \(PR\) and \(QR\) of  \(\Delta PQR\) such that  \( \angle P{\rm{ }} = \angle RTS\). Show that

Diagram

Text Solution

Reasoning:

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

This is referred as \(AA\) criterion for two triangles.

Steps:

In \(\Delta RPQ,\,\,\Delta RTS\)

\[\begin{align}  & \angle RPQ=\angle RTS\,\,\,\,\left( \text{given} \right) \\  & \angle PRQ=\angle TRS\,\,\left( \begin{array}  & \text{common} \\\text{angle} \\ \end{array} \right) \\  & \Rightarrow \Delta RPQ-\Delta RTS\left( \begin{array}& \because \,AA \\ 
  \text{criterion} \\ \end{array} \right) \\ \end{align}\]