Folks, below is the diagram that you must use to prove the concurrence of the altitudes of a triangle. Remember that the dotted lines are generated by making auxiliary lines from the vertices of the triangle such that each line is parallel to the side opposite each vertex. These auxiliary lines form a triangle of their own. Now, remember that your proof cannot
(a) assume the concurrence of the altitudes when proving precisely that and
(b) will employ the use of the theorem that the perpendicular bisectors of a triangle are concurrent at a point that is equidistant from the vertices.
Note: Please do not look at the book for this proof; you'll take all the fun out of proving it yourself!
6 comments:
Any thoughts on how to use the perpendicular bisectors are concurrent?
I have no idea what to do.
Anyone have advice?
Can we please use our real names when using the blog!!
I proved it by beginning with the giant triangle and constructing the smaller triangle such that its vertices are the midpoints of each side of the giant triangle. From there, you have the necessary givens to prove it.
Brilliant work Scott, you've understood the motivation behind the giant triangle. You see, the way I suggested to make the giant one, would in any case result in the triangle you talk of. Our midpoint theorem about any line connecting two midpoints of a triangle being parallel to the third side is how you know that the giant triangle, if constructed the way I suggested, would result in what you suggested the triangle should be.
Anyway, enough said, I'm proud of you and be ready to talk more about your progress in class.
Also, I think Scott may have a good hunch about the identity of the impostor squared.
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