Results 1 to 4 of 4

Math Help - More Triangles

  1. #1
    Junior Member whytechocolate01's Avatar
    Joined
    Apr 2007
    From
    On A Cloud Over There Somewhere
    Posts
    46

    Post More Triangles

    Please help me solve this!

    Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.

    Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB

    To Prove: Line CD bisects Angle ACB

    Plan: __________________________


    Proof:


    Statements: ___________________



    Reasons: ______________________
    Attached Thumbnails Attached Thumbnails More Triangles-triangle-abc.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by whytechocolate01 View Post
    Please help me solve this!

    Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.

    Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB

    To Prove: Line CD bisects Angle ACB

    Plan: __________________________


    Proof:


    Statements: ___________________



    Reasons: ______________________
    In the isosceles triangle ABC, we assume that it is sides AC and BC that
    are equal.

    angle CDA = angle CDB and both are right angles, as CD is an altitude
    from AB to C.

    angle CAD = angle CBD as they are the angles opposite the equal sides
    of an isosceles triangle.

    angle ACD = angle DCB as these are the third angles in two triangles whose
    other two angle are equal and so equal because the angle sum of any
    triangle is two right angles.

    Therefore as side CD is common to both triangle ACD and triangle BCD
    these triangles are congruent by ASA.

    Hence AD is congruent to DC as these are corresponding sides of congruent
    triangles. So we have proven that D bisects AC.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member whytechocolate01's Avatar
    Joined
    Apr 2007
    From
    On A Cloud Over There Somewhere
    Posts
    46

    :( Still confused...

    Uhm...i'm still confused. Which are the statements and reasons? And why? How did you get to that? I'm sorry math is not my strongest point but this is a really important assignment. Please be patient with me. I'm sorry for the trouble. But i'm so confused. Please explain more thoroughly if it's not too much trouble. Thank you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by whytechocolate01 View Post
    Please help me solve this!

    Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.

    Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB

    To Prove: Line CD bisects Angle ACB
    Plan: Prove that angle ACD is congruent to angle BCD

    1. ADC and BDC are triangles
    2. CDA and CDB are right angles (altitudes make right angles)
    3. CAD and CBD are congruent (It's an isosceles triangle)
    4. 180 - CDA - CAD = ACD (angles in a triangle add to 180)
    5. 180 - CDB - CBD = BCD (angles in a triangle add to 180)
    6. 180 - CDA -CAD = BCD (substitution)
    7. ACD = BCD (Transitive property)
    8. ACD and BCD are congruent
    9. CD bisects ACB (A line separating two equal angles is a bisector)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: March 19th 2011, 04:42 AM
  2. Triangles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 8th 2011, 10:37 AM
  3. Triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 12th 2009, 05:59 AM
  4. triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 24th 2009, 07:06 AM
  5. How Many Different Triangles?
    Posted in the Geometry Forum
    Replies: 0
    Last Post: October 16th 2008, 06:29 PM

Search Tags


/mathhelpforum @mathhelpforum