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Ex.7.4 Q3 Triangles Solution - NCERT Maths Class 9

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Question

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

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

 Video Solution
Triangles
Ex 7.4 | Question 3

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

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

 Video Solution
Triangles
Ex 7.4 | Question 3
  
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