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Thread: Parallel lines and congruent segments question

  1. #1

    Parallel lines and congruent segments question

    Let's take quadrilateral, ABCD, where the following is given:

    AC is parallel to BD
    AB is perpendicular to BD
    AB is congruent to CD

    Given the above, is it correct to conclude that CD is also perpendicular to BD, since AB and CD are congruent.

    Screen Shot 2017-11-05 at 12.20.23 AM.jpg

  2. #2
    Elite Member
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    Quote Originally Posted by kanakku View Post
    Let's take quadrilateral, ABCD, where the following is given:

    AC is parallel to BD
    AB is perpendicular to BD
    AB is congruent to CD

    Given the above, is it correct to conclude that CD is also perpendicular to BD, since AB and CD are congruent.

    Screen Shot 2017-11-05 at 12.20.23 AM.jpg

    Yes

    But can you support your conclusion with geometric argument (with reference to well known theorems).
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Thanks for the confirmation. I guess that's where I have been struggling to connect the dots. Which theorems should be used.

  4. #4
    Where would I start on how to prove that conclusion ?

  5. #5
    Elite Member stapel's Avatar
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    Feb 2004
    Posts
    15,435

    Cool

    Quote Originally Posted by kanakku View Post
    Where would I start on how to prove that conclusion ?
    Different geometry courses get to different theorems (or rules) in different orders. What results have you learned recently?

    When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

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