In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

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

Go back to  'Ex.7.4'

## 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

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school