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Posted by Rana Name 4 years, 9 months ago (11017828)
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Sia ? 4 years, 9 months ago (6945213)
Democracy is a form of government in which the rulers are elected by the people. Democracy is a form of government in which:-
- Rulers elected by people take all major decisions.
- Elections offer a choice and fair opportunity to the people to change the current rulers.
- This choice and opportunity is available to all the people on an equal basis.
- The exercise of this choice leads to a government limited by basic rules of the constitution and citizen’s rights.
Posted by Madhav Dixit 4 years, 9 months ago (9230162)
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Sia ? 4 years, 9 months ago (6945213)
If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
Construction
Join the vertex B of {tex}\triangle{/tex}ABC to Q and the vertex C to P to form the lines BQ and CP and then drop a perpendicular QN to the side AB and also draw PM{tex}\perp{/tex}AC as shown in the given figure.
Proof
Now the area of {tex}\triangle{/tex}APQ = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} AP {tex}\times{/tex} QN (Since, area of a triangle = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} Base {tex}\times{/tex} Height)
Similarly, area of {tex}\triangle{/tex}PBQ = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} PB {tex}\times{/tex} QN
area of {tex}\triangle{/tex}APQ = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} AQ {tex}\times{/tex} PM
Also, area of {tex}\triangle{/tex}QCP = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} QC {tex}\times{/tex} PM ...(i)
Now, if we find the ratio of the area of triangles {tex}\triangle{/tex}APQand {tex}\triangle{/tex}PBQ, we have
{tex}\frac{\text { area of } \Delta A P Q}{\text { area of } \Delta P B Q}{/tex} = {tex}\frac{\frac{1}{2} \times A P \times Q N}{\frac{1}{2} \times P B \times Q N}=\frac{A P}{P B}{/tex}
Similarly, {tex}\frac{\text { area of } \Delta A P Q}{\text { area of } \Delta Q C P}{/tex} = {tex}\frac{\frac{1}{2} \times A Q \times P M}{\frac{1}{2} \times Q C \times P M}=\frac{A Q}{Q C}{/tex} ...(ii)
According to the property of triangles, the triangles drawn between the same parallel lines and on the same base have equal areas.
Therefore, we can say that {tex}\triangle{/tex}PBQ and {tex}\triangle{/tex}QCP have the same area.
area of {tex}\triangle{/tex}PBQ = area of {tex}\triangle{/tex}QCP ...(iii)
Therefore, from the equations (i), (ii) and (iii) we can say that,
{tex}\frac{{AP}}{{PB}} = \frac{{AQ}}{{QC}}{/tex}
Also, {tex}\triangle{/tex}ABC and {tex}\triangle{/tex}APQ fulfil the conditions for similar triangles, as stated above. Thus, we can say that {tex}\triangle{/tex}ABC {tex} \sim {/tex} {tex}\triangle{/tex}APQ.
The MidPoint theorem is a special case of the basic proportionality theorem.
According to mid-point theorem, a line drawn joining the midpoints of the two sides of a triangle is parallel to the third side.
Posted by Anand Kumar 4 years, 9 months ago (10930929)
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Sia ? 4 years, 9 months ago (6945213)
Assembler is a program that translates the program from assembly to machine.
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Abul Fazal was one of the nine navratans of Akbar. He wrote the Akbarnama which is based on the actual descriptions of the events, royal documents and the oral testimonies of knowledgeable persons.
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Yug Kalpeshkumar Dabgar 4 years, 9 months ago (11035895)
2 Thank You