# Ex.7.2 Q3 Triangles Solution - NCERT Maths Class 9

## Question

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

## Text Solution

**What is known?**

Sides \(AB=AC,\)

\(BE\bot AC\ \text{and CF}\bot \text{AB}\)

**To prove:**

Altitudes \(BE\) and \(CF\) are equal or \(BE = CF\)

**Reasoning:**

We can show two triangles \(ABE\) and \(ACF\) congruent by using AAS congruency rule and then we can say corresponding parts of congruent triangles will be equal.

**Steps:**

\(\text{In } \Delta AEB \text{ and } \Delta AFC,\)

\[\begin{align}& \angle AEB = \angle AFC \;(\text{Each }90^{\circ}) \\ & \angle A = \angle A\; (\text{Common angle}) \\ & AB = AC\; (\text{Given}) \\ & \therefore \Delta AEB \cong \Delta AFC \\& \text{(By AAS congruence rule)} \end{align}\]

\(\therefore BE = CF\) (By \(CPCT\) )