Similarity and Congruence

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Pythagorean Theorem

Pythagoras' Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 BC and 500 BC.


Pythagoras' Theorem states that:


In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is:


KOER Triangles html m2f096af4.png


KOER Triangles html 4bd439df.png



Pythagoras' Theorem in Three Dimensions


A three-dimensional object can be described by three measurements - length, width and height.


KOER Triangles html 679fe2f6.pngKOER Triangles html m570261d2.png


We can use Pythagoras' Theorem to find the length of the longest straw that will fit inside


the box or cylinder.


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Teachers Corner

Suchetha . S. S Asst. Teacher ( Mathematics ) GJC Thyamagondlu. Nelamangala Talluk Bangalore Rural District doing a lesson on similar triangles using GeoGebra in the classroom

KOER Triangles html m3d25043b.jpg


GeoGebra Contributions

  1. The GeoGebra file below to understand Similar Triangles
    1. Similar Triangles Part 1 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_1.html
    2. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_1.ggb
    3. Similar Triangles Part 2 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_2.html
    4. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_2.ggb
    5. Similar Triangles Part 3 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_3.html
    6. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_3.ggb
    7. See a video to understand this concept http://www.youtube.com/watch?v=BI-rtfZVXy0
  1. The GeoGebra file below verifies the Thales theorem
    1. Thales Theorem http://www.karnatakaeducation.org.in/KOER/Maths/thales_theorem.html
    2. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/thales_theorem.ggb
    3. See a video that proves this theorem http://www.youtube.com/watch?v=Y-6yYsuGLoc

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