Saturday, September 26, 2015

Finding Isosceles Triangles

Finding Isosceles Triangles

Triangles
 
Karl's picture is here:
Isosceles Triangles
Bob draws this picture:

 Finding Isosceles Triangles


Now, you find a general solution (a generic method)!







Answer to Chameleons' Puzzle
 





Answer:
Answer to Finding Isosceles Triangles
  1. We can see that Monika's triangle is isosceles in several ways. We will show that |AC|=|BC|. We can use the Pythagorean Theorem to check that these both have length 22+32. In the calculations below M=(3,1) is the midpoint of AB¯¯¯¯¯¯¯¯.

    |AC|2|BC|2=|AM|2+|MC|2=22+32=|BM|2+|MC|2=22+32.
    We can also observe that to get from A to C we go over (to the right) by two units and then up three units. To get from B to C we go over (to the left) by two units and then up three units. We travel the same distance to get from A or B to C so A and B are equidistant from C. Finally, we can draw the horizontal line of symmetry for ABC.


    Isosceles triangles are exactly those triangles with a line of symmetry so ABCmust be isosceles.
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Brain Workout: Variety Puzzles to Boost Your Memory and Brainpower presents more than two hundred puzzles and mental tests that cover a variety of different themes, styles, and difficulty levels. This collection has been developed by author G. R. Roosta to stimulate and challenge the key components of the brain that control reasoning, language, logic, visual perception, attention, and flexibility. Brain Workout includes fun and challenging activities and mental exercises to help you get your brain in shape and keep it healthy. The puzzles included here are specifically designed to improve memory, attention, and speed, as well as the spatial, verbal, and numerical capabilities of your brain. Studies have shown that puzzles and mental exercises can improve brainpower by stimulating creativity and imagination, along with the analytical, rational, and logical areas of the brain. You can achieve great results with these puzzles by solving ten or more puzzles each day. Stimulate your mind and boost your brainpower through the mental gymnastics of the Brain Workout.



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