Results 1 to 5 of 5

Math Help - Congruent triangles

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    81

    Congruent triangles

    hi all attached is a question and answer from an exam paper which i am having trouble with.

    firstly i do not see how they can state the ASA rule without further information.

    secondly i would have drawn the perpendicular bisector of line YZ and labelled the point of intersection with YZ as W then stated

    YW = WZ (common)
    XW (common)
    XY=XY (given XYZ isoscles triangle)

    therefore triangle congruent SSS

    any ideas please?
    Attached Thumbnails Attached Thumbnails Congruent triangles-congruence-answer.jpg   Congruent triangles-congruence-question.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Like a stone-audioslave ADARSH's Avatar
    Joined
    Aug 2008
    From
    India
    Posts
    726
    Thanks
    2
    Quote Originally Posted by sammy28 View Post
    hi all attached is a question and answer from an exam paper which i am having trouble with.

    firstly i do not see how they can state the ASA rule without further information.

    secondly i would have drawn the perpendicular bisector of line YZ and labelled the point of intersection with YZ as W then stated

    YW = WZ (common)
    XW (common)
    XY=XY (given XYZ isoscles triangle)

    therefore triangle congruent SSS

    any ideas please?
    For the first thing -What more information were you expecting, can you be little specific


    Second thing-You have proved that YXW is congruent to ZXW
    I guess you wanted to add some more --
    Can you be a little more specific

    Are you trying to find the ways of proving it other than those given
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    81
    thanks ardash, i made a mistake in proving wrong triangles congruent

    if you label the intersection of segments NZ and YM, O; then
    for ASA to work i am thinking that angle ZYM = angle ZYX/2. but without extra given angles such as the angle at YNZ and the angle OYN or the angle YOZ then i dont see how to prove.

    even if i were to draw a circle radius OY centre O then extend line segment YM to the circumferance i get the circle thm. ' the angle of a semi circle is a right angle', but this is no use to this problem.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    You want to prove that triangles YMZ and ZNY are congruent using ASA rule.

    It means that you need to show that :
    1) angle NYZ = angle MZY
    2) angle NZY = angle MYZ
    3) side YZ = side YZ

    1) triangle XYZ is isosceles with XY = XZ therefore angle XYZ = angle XZY
    But N is on the segment [XY] therefore angle XYZ = angle NYZ
    and M is on the segment [XZ] therefore angle XZY = angle MZY
    Therefore angle NYZ = angle MZY

    2) is given by construction of M and N

    3) is of course evident

    ASA rule shows that triangles YMZ and ZNY are congruent
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2009
    Posts
    81
    thanks rg. i see my mistake now you point it out so clearly
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Congruent triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 28th 2010, 04:18 PM
  2. Congruent Triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 23rd 2010, 04:16 AM
  3. Congruent Triangles
    Posted in the Geometry Forum
    Replies: 6
    Last Post: December 29th 2008, 10:21 PM
  4. Congruent Triangles
    Posted in the Geometry Forum
    Replies: 6
    Last Post: November 25th 2008, 11:09 PM
  5. Sides of Congruent Triangles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 18th 2008, 07:29 PM

Search Tags


/mathhelpforum @mathhelpforum