15. Five mark exercise problems III

 

In the given figure, \(\triangle ABC\) is right-angled at \(C\) and \(DE \perp AB\). Prove that \(\triangle ABC \sim \triangle ADE\) and hence find the lengths of \(AE\) and \(DE\).

 

Answer:

 

(i) In \(\Delta ABC\) and \(\Delta ADE\):

 

 

 

\(\Delta ABC\) not similarsimilar \(\Delta ADE\)

 

(ii) The length of \(AE\) is $\frac{i}{i}$ \(cm\).

 

The length of \(DE\) is $\frac{i}{i}$ \(cm\).

 

 

2. Two triangles \(QPR\) and \(QSR\), right angled at \(P\) and \(S\) respectively are drawn on the same base \(QR\) and on the same side of \(QR\). If \(PR\) and \(SQ\) intersect at \(T\), prove that \(PT \times TR = ST \times TQ\).

 

Answer: