Picture Proof of Thales' Theorem of a right angle triangle inscribed in a semi-circle. скачать в хорошем качестве

Picture Proof of Thales' Theorem of a right angle triangle inscribed in a semi-circle.

This picture proof is approved of Thales theorem that states that when a triangle is inscribed in a circle with the diameter as one up at sides, it always produces a right angle opposite the diameter. Basically, if a triangles is inscribed, meaning its points are on a circle, and it uses the diameter for one of its sides, it’s a right triangle. We start this proof by drawing the inscribed triangle. From this point, we draw a line from the center to the apex of that triangle, bringing attention that we know at least three of the line segments are equal because they are radiuses of the circle. Because the line segments are equal, we know that both of the triangles we have just divided our isosceles triangles. With this being true, then the “bottom “angles of these isosceles triangles are equal to themselves. This means that in the larger triangle that we originally inscribed in the circle, that we have two angles of one measurement and two angles of another measurement. Because we know that the internal angles of a triangle add to 180°, then these four angles add to 180°. I’ve color-coded these angles, yellow, and purple, so that you can see them more easily. If we have two yellows and two purples to add to 180°, then it makes sense that one yellow and one purple would add to 90°. You’ll notice that the Apex angle of the larger triangle is made up of one yellow and one purple. This means that the Apex angle is always 90°. It doesn’t really matter where we put the Apex on the circle, we’re always going to end up with 90°. Try it! Move your Apex around, notice, how the angles shift with the movement of the Apex, and tell me what you notice! You can also find me at: The Beauty of Play -- https://thebeautyofplay.com Instagram --   / beauty_of_play   @beauty_of_play Facebook --   / beautyofplay   Pintrest --   / dellaparker.  .