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

 \[\begin{align}\angle R P Q&=\angle R T S \quad \text { (given) } \\ \angle P R Q&=\angle T R S \quad  \text { (Commonangle) } \\ \Rightarrow\qquad \Delta R P Q &- \Delta R T S \quad  \because \text { (AA criterion) }\end{align}\]