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

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

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