Ex.6.3 Q11 Triangles Solution - NCERT Maths Class 10


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 \(\Delta A B D \sim \Delta E C F\).


 Video Solution
Ex 6.3 | Question 11

Text Solution


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.


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

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

Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school