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

 Video Solution
Triangles
Ex 6.3 | Question 5

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

\[\begin{align} & \angle RPQ=\angle RTS\,\,\,\,( \text{Given} ) \\ & \angle PRQ=\angle TRS\\&(  \text{Common Angle} ) \\\\ & \Rightarrow \Delta RPQ-\Delta RTS\\&( \because \, \text{AA Criterion}) \\ \end{align}\]