# 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}

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