NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles

Exercise 6.2

Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reasons.

It is given that \(\triangle DEF \sim \triangle RPQ\). Is it true that \(\angle D=\angle R\) and \(\angle F=\angle P\)? Why?

Points \(A\) and \(B\) lie on sides \(PQ\) and \(PR\) of \(\triangle PQR\) such that \(PQ=12.5\,\text{cm}\), \(PA=5\,\text{cm}\), \(PB=4\,\text{cm}\) and \(BR=6\,\text{cm}\). Is \(AB\parallel QR\)? Give reasons.

In Fig. 6.4, \(BD\) and \(CE\) intersect each other at \(P\). Is \(\triangle PBC \sim \triangle PDE\)? Why?

In triangles \(PQR\) and \(MST\), \(\angle P=55^\circ,\; \angle Q=25^\circ\) and \(\angle M=100^\circ,\; \angle S=25^\circ\). Is \(\triangle QPR \sim \triangle TSM\)? Why?

Is the following statement true? Why?

“Two quadrilaterals are similar if their corresponding angles are equal.”

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of another triangle. Are the two triangles similar? Why?

If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?

The ratio of the corresponding altitudes of two similar triangles is \(\dfrac{3}{5}\). Is it correct to say that ratio of their areas is \(\dfrac{6}{5}\)? Why?

Point \(D\) is on side \(QR\) of \(\triangle PQR\) with \(PD\perp QR\). Is \(\triangle PQD \sim \triangle RPD\)? Why?

In Fig. 6.5, if \(\angle D = \angle C\), is it true that \(\triangle ADE \sim \triangle ACB\)? Why?

Is the following statement always true? “If an angle of one triangle equals an angle of another and two sides of one triangle are proportional to the corresponding two sides of the other triangle, then the triangles are similar.” Give reasons.