Answer
384.6k+ views
Hint: To prove $AD< BC$, we are going to use the property which says that the side opposite to the larger angle is longer and we will apply this property on to the angles A and angle B and then sides opposite to those angles. Also, we are going to apply this property onto the angles C and angle D and sides opposite to those angles.
Complete step by step solution:
The figure given in the above problem is as follows:
It is given that $\angle B<\angle A$ so side opposite to angle B is AO and side opposite to angle A is BO then we are going to apply the property that side opposite to larger angle is longer side so angle A is the larger angle as compared to angle B so side opposite to angle A (i.e. BO) is longer than side AO which is opposite to angle B.
$AO< BO$ ………… (1)
Similarly, we are going to apply the same property on angles C and D. It is given that $\angle C<\angle D$ so the side opposite to angle D (i.e. OC) is longer than side opposite to angle C (i.e. OD).
$OD< OC$ ……… (2)
Adding (1) and (2) we get,
$AO+OD< BO+OC$
From the above figure, we can see that:
$\begin{align}
& AO+OD=AD; \\
& BO+OC=BC \\
\end{align}$
So, using the above relations in the above inequality we get,
$AD Hence, we have shown that $AD< BC$.
Note: Just like in the above problem, we have shown that the side opposite to the larger angle is longer. Similarly, sides opposite to equal angles are equal. Also, the side opposite to the shorter angle is small in size as compared to the side opposite to the larger angle.
Complete step by step solution:
The figure given in the above problem is as follows:
![seo images](https://www.vedantu.com/question-sets/64dbf722-83a2-4d44-a63c-4d89f0b1443e1046063344186980366.png)
It is given that $\angle B<\angle A$ so side opposite to angle B is AO and side opposite to angle A is BO then we are going to apply the property that side opposite to larger angle is longer side so angle A is the larger angle as compared to angle B so side opposite to angle A (i.e. BO) is longer than side AO which is opposite to angle B.
$AO< BO$ ………… (1)
Similarly, we are going to apply the same property on angles C and D. It is given that $\angle C<\angle D$ so the side opposite to angle D (i.e. OC) is longer than side opposite to angle C (i.e. OD).
$OD< OC$ ……… (2)
Adding (1) and (2) we get,
$AO+OD< BO+OC$
From the above figure, we can see that:
$\begin{align}
& AO+OD=AD; \\
& BO+OC=BC \\
\end{align}$
So, using the above relations in the above inequality we get,
$AD
Note: Just like in the above problem, we have shown that the side opposite to the larger angle is longer. Similarly, sides opposite to equal angles are equal. Also, the side opposite to the shorter angle is small in size as compared to the side opposite to the larger angle.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)