# Ex.6.3 Q11 Triangles Solution - NCERT Maths Class 10

## Question

In Figure \(, E\) is a point on side \(CB\) produced of an isosceles \(\triangle ABC\) with \(AB = AC\). If \(AD \bot BC\) and \(EF \bot AC\), prove that \(\Delta A B D \sim \Delta E C F\).

**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 the \(AA\) criterion for two triangles.

**Steps:**

In \(\Delta ABD,\,\,\Delta ECF \)

\[\begin{align}&\angle ADB=\angle EFC={{90}^{\circ }}\\& (\because AD\bot BC \text{and}\,EF\bot AC) \\ &\angle ABD=\angle ECF \\& \begin{bmatrix}\because \text{In}\,\Delta ABC,AB=AC\\\Rightarrow \angle ABC=\angle ACB\end{bmatrix} \\&\Rightarrow \Delta ABD \sim \Delta ECF\\&\qquad(\text{AA}\,\,\text{criterion}) \\ \end{align}\]