Results 1 to 5 of 5

Math Help - Simple vector question

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    56

    Simple vector question

    Let O be the the origin. OA means O to A and so on.

    So if OD+OE+OF = 4(OA+OB+OC) , then △DEH is congurent to △ABC? Is this statement correct? If yes, why? How do we prove it? If no, how can i prove that the 2 triangles are congruent?

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,091
    Thanks
    315

    Re: Simple vector question

    To be congruent the two triangles must have the same size and shape. If the lengths of the sides of triangle DEF add up to be 4 times longer than the lengths of the sides of triangle ABC they are not congruent. In addition, even if the lengths did add up to be the same you still wouldn't know whether the triangles are congruent without knowing whether the individual lengths are identical.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Simple vector question

    A couple of thoughts:

    1. What is H?
    2. On the face of it, I would definitely claim that congruency does not follow from the given equation. Assuming you meant triangle DEF congruent to triangle ABC, suppose you had OD = OE = OF = 4, and it was an equilateral triangle (that's not even required from those equations, but let's suppose that's the case). Now suppose OA = 0.5, OB = 1.5, and OC = 1. Then the equation holds, but you can see that congruency does not have to hold. Essentially, the problem is that the equations you are given do not place any constraint whatsoever on the angles of the triangle.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2011
    Posts
    56

    Re: Simple vector question

    How bout if it is given OD=2OA+OB+OC, OE=OA+2OB+OC, and OF=OA+OB+2OC,such that ABC and DEF are two triangles in the plane and O is the origin? How can i prove that △ABC and △DEF are congruent?

    Actually, in vector, what conditions make 2 triangles congruent?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,091
    Thanks
    315

    Re: Simple vector question

    The example you gave does indeed yield triangles ABC and DEF being congruent - it's not too difficult to show that length AB = length DE, length AC = length DF, and length BC = length DE. But the general case of (OD +OE+OF) = 4(OA+OB+OC) does not yield congruent triangles. For example if A = (1,0), B= (-1,0), and C=(1,1) you have (OA+OB+OC) = 1. then you could set D=(1,0), E=(-1,0), and F = (4,1), so that OD+OE+OF = 4. DEF meets the condition specified, but is not congruent to ABC.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple vector question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 3rd 2011, 11:55 PM
  2. Simple question about vector.
    Posted in the Calculus Forum
    Replies: 9
    Last Post: September 21st 2010, 07:38 AM
  3. Simple vector question.
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 8th 2010, 10:04 PM
  4. Simple Vector question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 16th 2010, 02:00 AM
  5. Simple vector question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 17th 2010, 11:16 PM

Search Tags


/mathhelpforum @mathhelpforum