Results 1 to 4 of 4

Math Help - euclidean geometry! help

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    85

    euclidean geometry! help {solved}

    Suppose that in a triangle ABC the angle ABC=angle ACB show that side AB=AC. In triangle ABC let X lie on BC in such a way that angle AXB is a right angle. Show X is the midpoint of BC.


    ok its clearly isosceles so i thought mentioning Angle-side-angle then to show right angle i got confused where to go!
    Last edited by skystar; June 8th 2008 at 11:50 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2008
    Posts
    85
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by skystar View Post
    Suppose that in a triangle ABC the angle ABC=angle ACB show that side AB=AC. In triangle ABC let X lie on BC in such a way that angle AXB is a right angle. Show X is the midpoint of BC.


    ok its clearly isosceles so i thought mentioning Angle-side-angle then to show right angle i got confused where to go!
    Since triangle ABC is isosceles, and \overline{AB}\cong{\overline{AC}} \; \; and \; \; \angle {B} \cong{\angle{C}} \; \; then \; \; \triangle{ABX}\cong{\triangle{ACX}} by AAS (angle-angle-side) or HL (hypotenuse-leg) theorems.

    \overline{CX} \cong{\overline{BX}} by CPCTC (Corresponding Parts of Congruent Triangles are Congruent.

    X is the midpoint by definition of midpoint.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

    Since we knew that \angle{B}\cong{\angle{C}} \; \; then \; \; we \; \;conclude \; \;that \; \; \overline{AB}\cong{\overline{AC}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euclidean Geometry
    Posted in the Geometry Forum
    Replies: 5
    Last Post: November 19th 2010, 12:00 AM
  2. Euclidean geometry...subgroups
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 27th 2010, 08:26 AM
  3. geometry -Euclidean
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 6th 2008, 01:44 PM
  4. non-Euclidean Geometry Proof
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 2nd 2008, 03:20 PM
  5. Help me with Angles-Euclidean Geometry
    Posted in the Geometry Forum
    Replies: 3
    Last Post: September 3rd 2007, 03:48 PM

Search Tags


/mathhelpforum @mathhelpforum