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Math Help - Triangle in a square

  1. #1
    Member GAdams's Avatar
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    Triangle in a square

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    The equilateral triangle inside the square. Find angle DEC.

    I've had a long look at it and can't find the answer. I've found a lot of other angles but not the one I need!

    Any help appreciated
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by GAdams View Post
    Attached (not to scale)

    The equilateral triangle inside the square. Find angle DEC.

    I've had a long look at it and can't find the answer. I've found a lot of other angles but not the one I need!

    Any help appreciated
    Hello GAdams,

    I've attached a figure with some angles filled in. Can you find your missing angle from this? Remember that the base angles of an isosceles triangle are congruent.
    Attached Thumbnails Attached Thumbnails Triangle in a square-box.jpg  
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  3. #3
    Member GAdams's Avatar
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    Thanks for you reply, but I can't see the diagram to clearly.
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    A riddle wrapped in an enigma
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    Quote Originally Posted by GAdams View Post
    Thanks for you reply, but I can't see the diagram to clearly.
    Click on the diagram and it will enlarge.
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    Member GAdams's Avatar
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    Quote Originally Posted by masters View Post
    Click on the diagram and it will enlarge.
    I tried that, bit it doesn't get any bigger. However, from what I can tell, you seem to be showing that the side of teh square is the same as the side of the equaliater triangle.....omg, of course it is!! Sorry, actually had the eureka moment as I was typing this.

    Got it now.

    Thanks!!!
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  6. #6
    A riddle wrapped in an enigma
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    Quote Originally Posted by GAdams View Post
    I tried that, bit it doesn't get any bigger. However, from what I can tell, you seem to be showing that the side of teh square is the same as the side of the equaliater triangle.....omg, of course it is!! Sorry, actually had the eureka moment as I was typing this.

    Got it now.

    Thanks!!!
    Great! Now, I've included a better image for you to see.
    Attached Thumbnails Attached Thumbnails Triangle in a square-box.jpg  
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    Quote Originally Posted by masters View Post
    Great! Now, I've included a better image for you to see.
    i wanna ask how do u know that AD=AE & BC=BE_______to get thatDAe is isoscles....thnx
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    Quote Originally Posted by lebanon View Post
    i wanna ask how do u know that AD=AE & BC=BE_______to get thatDAe is isoscles....thnx
    Hello lebanon,

    We are told that the triangle is equilateral (all sides are congruent). One side of the equilateral triangle is on the square. So this means the sides of the square are congruent to the sides of the triangle.

    Look at the markings I have made on the sides of the triangle and square, indicating which triangles formed are isosceles. It should be pretty apparent if you know anything about isosceles triangles.
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