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Theorem 6.8 states that, In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. We have to prove this theorem.  Before proving we need to know theorem 6.7. Because we will use theorem 6.7 for proving theorem 6.8. Now theorem 6.7 states that, If a perpendicular is drawn from the vertex of the right angle triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other. It means that in a right triangle ABC right angled at B .when a perpendicular is drawn from angle B to AC then the two triangles formed namely as triangle ABD and triangle BDC are similar to each other and to whole triangle ABC. SO, NOW WE KNOW THE THEOREM 6.7 AND WITH THE HELP OF THIS THEOREM WE WILL PROVE THE THEOREM 6.8. To prove theorem 6.8, we are given a right triangle ABC right angled at B. To prove:  AC² = AB² + BC² Construction:  we have to construct a perpend...

In our body the air we inhale is taken through the nostrils. There are fine hairs in our nostrils, which filters the air passing through it.  Then the air passes through pharynx and larynx and goes into the lungs. In the lungs, the air passes into smaller and smaller tubes called Bronchi and Bronchioles. Then it finally reaches to a balloon-like structure called alveoli. In alveoli , exchange of gases takes place. The walls of alveoli contains a network of blood vessels.  The carbon-dioxide in our body is taken by blood and it releases into the alveoli and then goes out of the body through nostrils.  And the oxygenated air reached to alveoli is taken up by blood and transported to all the cells in the body.  If you want to know about Aerobic and Anaerobic respiration then go to the link given below.  Aerobic and Anaerobic respiration   And to know about Nutrition in humans go to this link  NUTRITION in HUMANS Please Subscribe t...

Respiration is of two types: (1) Aerobic Respiration and (2) Anaerobic Respiration.  Now, what is Aerobic respiration? When respiration takes place in the presence of oxygen, it is called Aerobic respiration.   What is Anaerobic respiration? When respiration takes place in the absence of oxygen, it is called Anaerobic respiration.  Now, the first step in Aerobic or Anaerobic respiration is to breakdown a six-carbon molecule (glucose) into a three- carbon molecule (pyruvate).  Now the breaking of pyruvate in Aerobic and Anaerobic respiration is different. In Aerobic respiration the pyruvate is break-down in presence of oxygen in mitochondria and it gives carbon-dioxide, water and energy.  Now, in Anaerobic respiration the pyruvate is break-down in absence of oxygen in cytoplasm and it gives carbon-dioxide, ethanol and energy.  In some cases the pyruvate is break-down in lack of oxygen in our muscles and it gives lactic acid and energy. It causes ...

Theorem 6.6 states that : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. We need to prove this theorem. Given:  Two similar triangles ABC and PQR. To prove:   ar(ABC)  = [AB] ² = [ BC] ²                   ar(PQR)    [ PQ ]       [QR]     = [ CA] ²        [RP] Constrution:  Draw two altitudes name as AM and PN of triangles.  Proof:  Area of triangle = 1/2 × base × height  So,  ar(ABC) = 1/2 × BC × AM  And ar(PQR) = 1/2 × QR × PN   Now, the ratio of both areas,         ar(ABC)  = 1/2 × BC × AM        ar(PQR)    1/2 × QR × PN             ar(ABC)  = BC × AM   (1)        ar(PQR)    QR × PN Now, in triangle ABM and PQN,   ...

The reactivity series is a series of metals in order of their reactivity. This means that the top metals of series will be more reactive than the bottom metals of series. Below is the reactivity series, in that potassium is the most reactive metal while gold is the least reactive.       How to remember this series? you can remember this series by this Extraction of Metals:       We have learnt about reactivity series above. By this series we can easily understand the extraction of metals.        Extraction of Metals low in reactivity series      Now, metals low in reactivity series are less reactive. They can be easily extracted from their oxides by only heating. For e.g. Cu2S can be obtained by just heating in air. Extraction of Metals middle in reactivity series:       The metals in the middle of the series are moderately reactive. They are present in natu...

   When we eat something we feel some water in our mouth. This is actually not water but a substance called saliva. Saliva is secreted from salivary glands. Saliva helps in making the food soft so it be easy to digest. The food we eat is in complex molecule and it has to be in simpler or smaller molecule. salivary amylase enzyme contained by saliva do this job. Then after chewing the food it goes down through food pipe or oesophagus.      The food then reaches to stomach. Stomach has digestive juices which help in digesting food. The wall of the stomach contains gastric glands which release hydrochloric acid, pepsin which digest proteins, and mucus. Pepsin needs an acidic medium to react so hydrochloric acid makes the medium acidic. And the mucus protects the inner lining of the stomach from the reaction of acid. When we eat more amount of food the stomach makes more hydrochloric acid and this cause pain and irritation ca...