which is the main occupation in kalaburagi division​

Answer:

5834 is divisible by 2

It is not divisible by 3 so it is not divisible by 6

35000 is divisible by 4

Answer:

this is answer

Explanation:

I hope you understand

क) संस्कृत भाषा प्राचीनतमा।

क) संस्कृत भाषा प्राचीनतमा।(ख) शून्यस्य प्रतिपादनं आर्यभटः अकरोत् ।

(ग) कौटिल्येन रचितं शास्त्रं अर्थशास्त्रं अस्ति।

(ग) कौटिल्येन रचितं शास्त्रं अर्थशास्त्रं अस्ति।(घ) संस्कृत भाषायाः काव्यसौन्दर्यम् अनुपमम्।

(ग) कौटिल्येन रचितं शास्त्रं अर्थशास्त्रं अस्ति।(घ) संस्कृत भाषायाः काव्यसौन्दर्यम् अनुपमम्।(ङ) संस्कृते विद्यमानाः सूक्तयः अभ्युदयाय प्रेरयन्ति

Question :- In triangle ABC, segment AD is perpendicular to BC. Prove that

[tex]\rm \: {AB}^{2} + {CD}^{2} = {BD}^{2} + {AC}^{2} \\ [/tex]

[tex]\large\underline{\sf{Solution-}}[/tex]

As it is given that

[tex]\rm \: AD \: \perp \: BC \\ [/tex]

[tex]\rm\implies \angle\:ADB \: = \: \angle ADC \: = \: 90 \degree \\ [/tex]

Now, in right angle triangle ADB

By using Pythagoras Theorem, we have

[tex]\rm \: {AB}^{2} = {AD}^{2} + {BD}^{2} \\ [/tex]

[tex]\rm\implies \: {AD}^{2} = {AB}^{2} - {BD}^{2} - - - (1) \\ [/tex]

Now, in right angle triangle ADC

By using Pythagoras Theorem, we have

[tex]\rm \: {AC}^{2} = {AD}^{2} + {CD}^{2} \\ [/tex]

[tex]\rm\implies \: {AD}^{2} = {AC}^{2} - {CD}^{2} - - - (2) \\ [/tex]

From equation (1) and (2), we get

[tex]\rm \: {AB}^{2} - {BD}^{2} = {AC}^{2} - {CD}^{2} \\ [/tex]

[tex]\rm\implies \:\boxed{ \rm{ \: {AB}^{2} + {CD}^{2} = {BD}^{2} + {AC}^{2} \: \: }} \\ [/tex]

Hence, Proved

[tex]\rule{190pt}{2pt}[/tex]

Additional Information :-

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem,

This theorem states that : - If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

by cancelling AD from right hand side we get BD square -CD square

and interchanging the position of negative segments we can prace this proof

that is the answer please check it