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    Is it ok if like you provide a simple explanation of the angle bisector theorem

    Module 2 Day 13 Challenge Part 4
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    • The Blade DancerT
      The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
      last edited by debbie

      Module 2 Week 4 Day 13 Challenge Explanation Part 3

      Is it ok if like you provide a simple explanation of the angle bisector theorem that say an 8 year old can understand?

      The Blade Dancer
      League of Legends, Valorant: Harlem Charades (#NA1)
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      debbieD 1 Reply Last reply Reply Quote 4
      • debbieD
        debbie ADMIN M0★ M1 M5 @The Blade Dancer
        last edited by debbie

        @TSS-Graviser

        I've drawn a little picture here of several triangles with angle bisector lines cutting the top-left angle. I hope this helps to visualize what Angle Bisector Theorem means.

        For all these triangles, please assume that the line going through the triangle bisects, or cuts the angle it comes out of, perfectly in half.

        M2W4D13-Ch-4-explain-angle-bisector.png

         
        Take a look at the top two sides of the triangle, colored \(\textcolor{green}{\text{green}}\) and \(\textcolor{red}{\text{red}}. \)

        Observe the ratio of the \(\textcolor{green}{\text{green}}\) and \(\textcolor{red}{\text{red}}\) sides. I have written this ratio below each triangle, e.g. \( 1:2, 1:3,\) etc.

        The Angle Bisector line cuts the bottom side of each triangle into two pieces. What if we want to know exactly how long these pieces are? Well, it's easy! See, if the ratio of the \(\textcolor{green}{\text{green}}\) and \(\textcolor{red}{\text{red}} \) sides is \(1:2,\) then the ratio of the pieces of the cut-up side are in that same ratio, \(1:2.\)

        Let me tell you about a very common mistake that some people might make. It's very common to think: "Oh, the \(\textcolor{red}{\text{red}} \) side is double the \(\textcolor{green}{\text{green}}\) side, so that means the third side gets cut in half, since that's \(\frac{1}{2}.\) 🅾 h no, be careful! If the \(\textcolor{red}{\text{red}} \) side is double the \(\textcolor{green}{\text{green}}\) side, then the \(\textcolor{green}{\text{green}}\) side is really \(\frac{1}{3}\) of the sum of the sides. That means the shorter segment of the cut-up side should be \(\frac{1}{3}\) of the total side length.
         
         
        M2W4D13-Ch-4-explain-angle-bisector-with-po.png
         
         
        I really would have loved to put a proof of the Angle Bisector Theorem here, but it uses some trigonometry and advanced geometry theorems. However, if you'd like to know, I'd be happy to write write it out, because it is surprisingly simple!

        🙂

        victorioussheepV 1 Reply Last reply Reply Quote 3
        • victorioussheepV
          victorioussheep M0★ M1★ M2★ M3★ M4 @debbie
          last edited by

          @debbie I still don't get how it is not 1/2 when the last picture is appearing a 1/2 ratio?😲

          quacker88Q 1 Reply Last reply Reply Quote 2
          • quacker88Q
            quacker88 MOD @victorioussheep
            last edited by

            Hey @victorioussheep! You are correct: on the long side, the ratio of the blue segment to the red segment is indeed 1:2. What the bubble is saying though, is that that blue segment is 1/3 of the WHOLE side, not just the red part.
            Hope this makes sense! 🙂

            victorioussheepV 1 Reply Last reply Reply Quote 2
            • victorioussheepV
              victorioussheep M0★ M1★ M2★ M3★ M4 @quacker88
              last edited by

              @quacker88 Oh...Now it makes sense😀 😳

              1 Reply Last reply Reply Quote 2

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