Results 1 to 7 of 7

Math Help - Congruent Triangles

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Congruent Triangles

    In the statement vs reasons chart, what is actually needed to prove that two triangles are congruent?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    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 magentarita View Post
    In the statement vs reasons chart, what is actually needed to prove that two triangles are congruent?
    This is a pretty broad question. Based on whatever the "Given" conditions are, one can prove congruency of triangles by:

    (1) SSS

    (2) SAS

    (3) ASA

    (4) AAS

    And if the triangles are right triangles you can throw in:

    (5) HL

    I'll leave you to look up the actual threorem (postulate) wording in conditional statement form.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,860
    Thanks
    742
    Hello, magentarita!

    In the statement vs reasons chart, what is actually needed
    to prove that two triangles are congruent?
    I refer to corresponding parts of two triangles.


    Code:
              C                     R
              *                     *
             *  .                  *  .
            *     .               *     .
           * θ      .            * θ      .
        A *  *  *  *  * B     P *  *  *  *  * Q
    If two sides and the included angle of one triangle
    . . equals two sides and the included angle of another triangle,
    . . the triangles are congruent.

    This is called "side-angle-side" or s.a.s.




    Code:
              .                     .
             .  .                  .  .
            *     *               *     *
           * α    β *            * α    β *
        A *  *  *  *  * B     P *  *  *  *  * Q
    If two angles and the included side of one triangle
    . . equals two angles and the included side of another triangle,
    . . the triangles are congruent.

    This is called "angle-side-angle" or a.s.a.




    Code:
              C                     R
              *                     *
             *  *                  *  *
            *     *               *     *
           *        *            *        *
        A *  *  *  *  * B     P *  *  *  *  * Q
    If three sides of one triangle are equal to three sides of another triangle,
    . . the triangles are congruent.

    This is called "side-side-side" or s.s.s.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    ok...........

    Quote Originally Posted by masters View Post
    This is a pretty broad question. Based on whatever the "Given" conditions are, one can prove congruency of triangles by:

    (1) SSS

    (2) SAS

    (3) ASA

    (4) AAS

    And if the triangles are right triangles you can throw in:

    (5) HL

    I'll leave you to look up the actual threorem (postulate) wording in conditional statement form.
    You said:

    "I'll leave you to look up the actual threorem (postulate) wording in conditional statement form." I thought a theorem is not a postulate, right?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    wonderful.........

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    I refer to corresponding parts of two triangles.


    Code:
              C                     R
              *                     *
             *  .                  *  .
            *     .               *     .
           * θ      .            * θ      .
        A *  *  *  *  * B     P *  *  *  *  * Q
    If two sides and the included angle of one triangle
    . . equals two sides and the included angle of another triangle,
    . . the triangles are congruent.

    This is called "side-angle-side" or s.a.s.



    Code:
              .                     .
             .  .                  .  .
            *     *               *     *
           * α    β *            * α    β *
        A *  *  *  *  * B     P *  *  *  *  * Q
    If two angles and the included side of one triangle
    . . equals two angles and the included side of another triangle,
    . . the triangles are congruent.

    This is called "angle-side-angle" or a.s.a.



    Code:
              C                     R
              *                     *
             *  *                  *  *
            *     *               *     *
           *        *            *        *
        A *  *  *  *  * B     P *  *  *  *  * Q
    If three sides of one triangle are equal to three sides of another triangle,
    . . the triangles are congruent.

    This is called "side-side-side" or s.s.s.
    This is fabulous information as always.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    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 magentarita View Post
    You said:

    "I'll leave you to look up the actual threorem (postulate) wording in conditional statement form." I thought a theorem is not a postulate, right?
    Actually, SSS, SAS, ASA, and HL are postulates, while AAS is a theorem.

    And there are other theorems regarding right triangles that can easily be proven from the postulates; namely, LL, LA, and HA. That's why I didn't name them. If you remember those 5 I originally stated, you'll be ok.

    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    ok...........

    Quote Originally Posted by masters View Post
    Actually, SSS, SAS, ASA, and HL are postulates, while AAS is a theorem.

    And there are other theorems regarding right triangles that can easily be proven from the postulates; namely, LL, LA, and HA. That's why I didn't name them. If you remember those 5 I originally stated, you'll be ok.
    I love geometry. It is my favoriye math topic.
    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: 4
    Last Post: April 7th 2009, 01:44 PM
  4. Congruent Triangles
    Posted in the Geometry Forum
    Replies: 6
    Last Post: December 29th 2008, 10:21 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