NCERT Solutions
Class 9 - Mathematics - Chapter 7: TRIANGLES

EXERCISE 7.2

In an isosceles triangle \(ABC\), with \(AB = AC\), the bisectors of \(\angle B\) and \(\angle C\) intersect each other at \(O\). Join \(A\) to \(O\). Show that: (i) \(OB = OC\), (ii) \(AO\) bisects \(\angle A\).

In \( \triangle ABC \), \(AD\) is the perpendicular bisector of \(BC\). Show that \( \triangle ABC \) is an isosceles triangle in which \(AB = AC\).

\(ABC\) is an isosceles triangle in which altitudes \(BE\) and \(CF\) are drawn to equal sides \(AC\) and \(AB\) respectively. Show that these altitudes are equal.

\(ABC\) is a triangle in which altitudes \(BE\) and \(CF\) to sides \(AC\) and \(AB\) are equal. Show that (i) \( \triangle ABE \cong \triangle ACF \), (ii) \(AB = AC\), i.e., \(ABC\) is an isosceles triangle.

\(ABC\) and \(DBC\) are two isosceles triangles on the same base \(BC\). Show that \(\angle ABD = \angle ACD\).

\(\triangle ABC\) is an isosceles triangle in which \(AB = AC\). Side \(BA\) is produced to \(D\) such that \(AD = AB\). Show that \(\angle BCD\) is a right angle.

\(ABC\) is a right-angled triangle in which \(\angle A = 90^\circ\) and \(AB = AC\). Find \(\angle B\) and \(\angle C\).

Show that the angles of an equilateral triangle are \(60^\circ\) each.