Geometry Honors 07-08 1st Semester

Wednesday, September 12, 2007

#3.7 Points of Concurrency

Aim 1: to construct the 3 angle bisectors of a triangle (incenter)
Aim 2: to construct the 3 perpendicular bisectors of a triangle (circumcenter)
Aim 3: to construct the 3 altitudes of a triangle (orthocenter)
Aim 4: to construct the 3 medians of a triangle (centroid)

  • You are to construct the 3 angle bisectors of an acute triangle.
  • then construct the 3 angle bisectors of an obtuse triangle.
  • then construct the 3 angle bisectors of a right triangle.
  • Repeat this for Aims 2, 3, and 4 above.
  • Be sure you label each triangle. For example: 3 Angle Bisectors of an Acute Triangle.
  • You should have 12 total triangles with you on Friday! I would use 6 sheets of paper and do one triangle on each side if i were you.
  • Also, finish whatever you didn't finish from last evening's homework assignment!
  • For those of you who think you're ready for the Mack Daddy Construction, draw a medium-large acute triangle. Then, construct the incenter, circumcenter, orthocenter, and centroid all in the same triangle. Yes, it will get kind of messy. Color pencils might help. 3 of these centers will be collinear (meaning they will line up in a straight line). Your mission, should you choose to accept it, will be to find which 3 centers are collinear.

posted by msichan at 9/12/2007 12:32:00 PM

4 Comments:

  • so im confuse what are the 12 angle or triangle are we constructing?

    By Blogger TNguyen, At September 12, 2007 at 9:26 PM  

  • we have to construct 3 angle bisectors for an acute triangle, then 3 angle bisectors with an obtuse triangle, then 3 angle bisectors with a right triangle. then we have to do the same thing but instead of angle bisectors we construct 3 perpendicular bisectors with an acute triangle and then with obtuse and right triangles. and then instead of perpendicular bisectors we construct with altitude. Then instead of alitude we construct with median of an acute, obtuse, and right triangles. so for every triangle you have to do 3.

    By Blogger molly, At September 13, 2007 at 10:10 AM  

  • hey dose any one know how to construc the median of a triangle?????

    By Blogger inukid, At September 13, 2007 at 6:34 PM  

  • Hey, Inukid.

    Sorry for the late reply, but if you still need a little help on constructing the median of a triangle, here's a head's up.

    Constructing a Median:

    Alright, so you know the definition of a median is a line segment from a vertex to the midpoint of the opposite side. The midpoint--that's the key to this construction. How do you find the midpoint of a line?

    You would construct a perpendicular, right?

    [[Ack. I can't seem to get the image HTML tags to function. Copy and past this link into your address bar:

    http://i6.tinypic.com/4vq97o1.jpg]]

    First thing's first, draw a triangle. I doodled triangle ABC on MS Paint. Let's construct a median from A to BC, okay? XD

    Construct a line perpendicular to side BC. To do that, take your compass and place the center on point B. I recommend that your radius should at least be greater than half of BC. Construct an arc.

    [[We're doing a fishie here. I did a full body fish in the picture, but it's probably better to show the arcs that intersect.]]

    After that, use the same radius and place the center of your compass on point C and construct another arc. Mark your points of intersection and connect them by drawing a line. The point where the line intersects with side BC is its midpoint.

    Now, just draw a line from vertex A to the midpoint--and walaaah! You've got your first median. :D

    Hope this was of use to you. XD

    Sincerely,
    --Mary.

    By Blogger M.Velasco, At September 13, 2007 at 8:02 PM  

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