# Ex.7.4 Q3 Triangles Solution - NCERT Maths Class 9

## Question

In the given figure, \(\angle B \lt \angle A\) and

\(\angle C \lt \angle D\). Show that \(AD \lt BC\).

## Text Solution

**What is Known?**

\[\angle \text{B}<\angle \text{A and }\angle \text{C}<\angle \text{D}\]

**To prove:**

\[\text{AD}<\text{BC}\]

**Reasoning:**

We can use the fact that In any triangle, the side opposite to the larger (greater) angle is longer We can add both the triangles result to get the required result.

**Steps:**

In \(\Delta AOB\),

\[\begin{align}&\angle B \lt \angle A\\ &AO \lt BO\\& \left(\begin{array}{}\text{Side opposite to the smaller}\\ \text{ angle is smaller} \ldots (1)\end{array}\right)\end{align}\]

In \(\Delta COD\),

\[\begin{align}&\angle C \lt \angle D\\ &OD \lt OC\\& \left(\begin{array}{}\text{Side opposite to the smaller}\\ \text{ angle is smaller} \ldots (2)\end{array}\right)\end{align}\]

On adding Equations (\(1\)) and (\(2\)), we obtain

\[\begin{align} & AO + OD \lt BO + OC \\ & AD \lt BC, \text{proved}\end{align}\]