Results 1 to 3 of 3

Math Help - Modern Geometry: Proving Angles Congruent

  1. #1
    Member ilikedmath's Avatar
    Joined
    Sep 2008
    Posts
    98

    Question Modern Geometry: Proving Angles Congruent

    If WS = WT and RS = ST = TU, with R-S-T-U, prove that ∠RWS TWU.

    My work so far:
    Proof:
    Given: WS
    = WT and RS = ST = TU, with R-S-T-U
    Given that R-S-T-U, we know R-S-T, S-T-U, R-S-U, and R-T-U.

    WST WTS by the Isosceles Triangle Theorem.
    m∠WST = mWTS by CPCF (Congruent Parts of Congruent Figures)

    m∠WSR + mWST = 180, and m∠WTU + mWTS = 180.

    m∠
    WSR = mWTU by algebra

    WSR WTU, and therefore,

    Triangle WSR
    Triangle WTU by SAS.

    And thus, RWS TWU
    by CPCF.

    ---
    Am I even close to having a legitimate proof? I'm pretty sure there is something missing since I did not use the given betweenness relation of R-S-T-U.
    Any corrections/suggestions, tips/help is greatly appreciated. Thank you very much for your time.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,661
    Thanks
    1616
    Awards
    1
    BIG HINT: Use the external angle theorem.
    m\left( {\angle WST} \right) = m\left( {\angle WRS} \right) + m\left( {\angle SWR} \right)\;\& \,m\left( {\angle WTS} \right) = m\left( {\angle WUT} \right) + m\left( {\angle TWU} \right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member ilikedmath's Avatar
    Joined
    Sep 2008
    Posts
    98

    Question Ok

    Quote Originally Posted by Plato View Post
    BIG HINT: Use the external angle theorem.
    My struggles with this class (Modern Geometry) is that it's like we basically have to forget everything we learned in our high school geometry class because we are "building up our repertoire" of tools to use for proofs. So in this case, I don't know if we can use the external angle theorem. (Our text is David Kay's College Geometry 2nd ed.)

    But anyway, if I can use the external angle theorem, I already know
     {\angle WST} =  {\angle WTS} since triangle WST is isosceles with WS = WT. So, since  {\angle WST} =  {\angle WTS}, then wouldn't their complements be equal by the theorem that "2 angles that are supplementary to the same angle have equal measures." And thus by, SAS (WS = WT,  {\angle WSR} =  {\angle WTU}, and RS = TU), triangles WSR and WTU are congruent; so  {\angle RWS} and  {\angle TWU} are also congruent by CPCF.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Having Trouble Proving These Angles Congruent
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 25th 2010, 03:15 PM
  2. Modern Geometry: Taxicab Geometry Problems
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 30th 2009, 07:32 PM
  3. Replies: 2
    Last Post: March 20th 2009, 09:21 AM
  4. Replies: 3
    Last Post: February 27th 2009, 12:30 PM
  5. Congruent Angles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 22nd 2008, 09:09 PM

Search Tags


/mathhelpforum @mathhelpforum