Ex.6.2 Q1 Triangles Solution - NCERT Maths Class 10

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Question

 In Figure , (i) and (ii), \(DE || BC.\) Find \(EC\) in (i) and \(AD\) in (ii)

                            

Text Solution

  

Reasoning:

As we all know the Basic Proportionality Theorem (B.P.T) or (Thales Theorem)

Two triangles are similar if :

(i) Their corresponding angles are equal

(ii) Their corresponding sides are in the same ratio (or proportion)

Steps:

(i) In\(\,\,\Delta ABC\) 

\[\begin{align} BC||DE \\ \end{align}\]

In\(\begin{align}\Delta ABC\,\,&\And \,\,\Delta ADE \end{align}\)

\[\begin{align}\angle ABC& =\angle ADE\,\,\left[ \because \,\text{corresponding}\,\text{angles} \right] \\ \angle ACB&=\angle AED\,\,\left[ \because \,\text{corresponding}\,\text{angles} \right] \\\angle A& =\angle A\,\,\text{common} \\ \!& \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\Rightarrow \Delta ABC\,\,\text{~}\,\,\Delta ADE \\ \end{align}\]

\[\begin{align} \frac{AD}{DB}&=\frac{AE}{EC} \\  \frac{1.5}{3}&=\frac{1}{EC} \\ EC&=\frac{3\times 1}{1.5} \\  EC&=2\,\text{cm}\end{align}\]

(ii) Similarly, \(\Delta ABC \sim \Delta ADE\)

\[\begin{align} \frac{AD}{DB}&=\frac{AE}{EC} \\ \frac{AD}{7.2} &=\frac{1.8}{5.4} \\ AD&=\frac{7.2\times 1.8}{5.4} \\ AD&=2.4\,\text{cm} \\\end{align}\]

  
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