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Neeraj Kumar 1 year, 9 months ago
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Vidit Chechani 1 year, 9 months ago
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Preeti Dabral 1 year, 9 months ago
Given: {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}DEF
AM is a median in {tex}\triangle {/tex}ABC and DN is the corresponding median in {tex}\triangle {/tex}DEF
To prove: {tex}\frac{{area\vartriangle ABC}}{{area\vartriangle DEF}} = \frac{{A{M^2}}}{{D{N^2}}}{/tex}
Proof: {tex}\triangle {/tex}DBC {tex} \sim {/tex} {tex}\triangle {/tex}DEF
{tex}\Rightarrow {/tex} {tex}\angle{/tex} A = {tex}\angle{/tex} D, {tex}\angle{/tex} B = {tex}\angle{/tex} E, {tex}\angle{/tex} C = {tex}\angle{/tex} F and
{tex}\frac{{AB}}{{DE}} = \frac{{BC}}{{EF}} = \frac{{AC}}{{DF}}{/tex}
Also, {tex}\frac{{area\vartriangle ABC}}{{area\vartriangle DEF}}{/tex}={tex}\frac{{A{B^2}}}{{D{E^2}}} = \frac{{B{C^2}}}{{E{F^2}}} = \frac{{A{C^2}}}{{D{F^2}}}{/tex}........(i)[area theorem]
Now,{tex}\frac{{AB}}{{DE}} = \frac{{BC}}{{EF}} = \frac{{\frac{1}{2}BC}}{{\frac{1}{2}EF}} = \frac{{BM}}{{EN}}{/tex}..............(ii)
In {tex}\triangle {/tex}ABM and DEN
{tex}\angle{/tex} B= {tex}\angle{/tex} E and {tex}\frac{{AB}}{{DE}} = \frac{{BM}}{{EN}}{/tex} [From (ii)]
{tex}\Rightarrow {/tex} {tex}\triangle {/tex}ABM {tex} \sim {/tex}{tex}\triangle {/tex}DEN [SAS similarity]
{tex}\Rightarrow {/tex}{tex}\frac{{area\vartriangle ABM}}{{area\vartriangle DEN}} = \frac{{A{B^2}}}{{D{E^2}}} = \frac{{A{M^2}}}{{D{N^2}}} = \frac{{B{M^2}}}{{E{N^2}}}{/tex}............(iii)
From (i) and (iii), we get
{tex}\frac{{area\vartriangle ABC}}{{area\vartriangle DEF}} = \frac{{A{M^2}}}{{D{N^2}}}{/tex}
Posted by Anna Bhai 1 year, 9 months ago
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Preeti Dabral 1 year, 9 months ago
The formula for the volume of a cone is V=1/3hπr². Learn how to use this formula to solve an example problem.
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Preeti Dabral 1 year, 10 months ago
A group of two or more than two atoms of the same or different elements that are chemically bonded together is called a molecule. For example: Two atoms of hydrogen (H2) and one atom of oxygen (O2) react with each other and form one molecule of water.molecule make up matter.
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Vedansh Gupta 1 year, 10 months ago
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Posted by Vedansh Gupta 1 year, 10 months ago
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Preeti Dabral 1 year, 10 months ago
It ended the monarchy in France and established democracy. It also caused other countries to declare war on France. Additionally, it led to the rise of Napoleon Bonaparte. Napoleon was a military general who became Emperor of France.
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Preeti Dabral 1 year, 9 months ago
The term carbon skeleton is used to describe the pattern in which the carbon atoms are bonded together in a molecule, disregarding atoms of other elements and differences between single and multiple bonds.
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Rahul Manda 1 year, 9 months ago
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Posted by Ritika Rathore 1 year, 9 months ago
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Preeti Dabral 1 year, 9 months ago
In 1848, Frdric Sorrieu, a French artist, prepared a series of four prints visualising his dream of a world made up of democratic and social Republics, as he called them.
Posted by Anushka Tetarwal 1 year, 9 months ago
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Preeti Dabral 1 year, 9 months ago
A direct-current (DC) generator is a rotating machine that supplies an electrical output with unidirectional voltage and current. The basic principles of operation are the same as those for synchronous generators.
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Preeti Dabral 1 year, 9 months ago
प्रत्येक देश का अपना संविधान होता है। संविधान उन मौलिक नियमों, सिद्धान्तों तथा परम्पराओं का संग्रह होता है, जिनके अनुसार राज्य की सरकार का गठन, सरकार के कार्य, नागरिकों के अधिकार तथा नागरिकों और सरकार के बीच सम्बन्ध को निश्चित किया जाता है। शासन का स्वरूप लोकतांत्रिक हो या अधिनायकवादी, कुछ ऐसे नियमों के अस्तित्व से इन्कार नहीं किया जा सकता जो राज्य में विभिन्न राजनीतिक संस्थाओं तथा शासकों की भूमिका को निश्चित करते हैं। इन नियमों के संग्रह को ही संविधान कहा जाता है।
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