Results 1 to 3 of 3

Math Help - Modern Geometry: Prove base angles of isosceles triangle are acute.

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

    Question Modern Geometry: Prove base angles of isosceles triangle are acute.

    Prove that the base angles of any isosceles triangle are acute.
    Given this figure:



    Here is my work so far:
    (So I need to show m
    ∠ACB < 90. And by showing that, I will also show that ∠B < 90 since ∠ACB ∠B since they are the base angles of an isosceles triangle.)

    Proof: Given isosceles triangle ABC.
    Extend segment BC to ray BD by construction.
    m∠ACB + m∠DCA = 180 by supplementary angle defn.
    Assume
    m∠ACB ≥ 90. ∠ACB ∠ABC by base angles of isosceles triangle are congruent.
    Then
    m∠ACB + m∠ABC ≥ 180, but then the angle measure of triangle ABC will be > 180 which is a C! (contradiction) since a triangle's total angle sum is 180.
    Therefore,
    m∠ACB < 90 and since ∠ACB ∠ABC, then also, m∠ABC < 90.
    Therefore, the base angles of any isosceles triangle are acute. QED.

    Is that an okay proof?

    Thank you for your time and help/suggestions/corrections.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    It's OK
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member ilikedmath's Avatar
    Joined
    Sep 2008
    Posts
    98
    Quote Originally Posted by running-gag View Post
    Hi

    It's OK
    Thank you!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that triangle ABC is isosceles
    Posted in the Geometry Forum
    Replies: 9
    Last Post: January 25th 2013, 10:48 AM
  2. Replies: 1
    Last Post: May 1st 2010, 08:37 AM
  3. Replies: 7
    Last Post: October 29th 2009, 08:48 AM
  4. Replies: 1
    Last Post: February 22nd 2009, 07:12 PM
  5. Modern Geometry: Proving Angles Congruent
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 22nd 2009, 05:27 PM

Search Tags


/mathhelpforum @mathhelpforum