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Math Help - Alternate Angles In Transversal

  1. #1
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    Question Alternate Angles In Transversal

    Please have a look at the attachment. Are the angles 3, 4, 8 & 9 interior angles? In other words, what are the exterior & interior angles when a transversal cuts 3 (or more) lines? Also the corresponding angle of angle 2 is angle 5. Why isn't angle 9 the corresponding angle of angle 2? Similarly the corresponding angle of angle 4 is angle 6. Why isn't angle 2 the corresponding angle of angle 4?

    Coming to the alternate angles - the alternate angle of angle 1 is angle 6. Why isn't angle 4 or angle 5 the alternate angle of angle 1? Similarly the alternate angle of angle 5 is angle 8. Why isn't angle 3 or angle 11 the alternate angle of angle 5?

    Thanks
    Attached Thumbnails Attached Thumbnails Alternate Angles In Transversal-transversal.jpg  
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  2. #2
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    Quote Originally Posted by rn5a View Post
    Please have a look at the attachment. Are the angles 3, 4, 8 & 9 interior angles? In other words, what are the exterior & interior angles when a transversal cuts 3 (or more) lines? Also the corresponding angle of angle 2 is angle 5. Why isn't angle 9 the corresponding angle of angle 2? Similarly the corresponding angle of angle 4 is angle 6. Why isn't angle 2 the corresponding angle of angle 4?

    Coming to the alternate angles - the alternate angle of angle 1 is angle 6. Why isn't angle 4 or angle 5 the alternate angle of angle 1? Similarly the alternate angle of angle 5 is angle 8. Why isn't angle 3 or angle 11 the alternate angle of angle 5?

    Thanks
    The terms "interior" and "exterior" angles, as well as "alternate" or "corresponding" angles only apply to the situation when a transversal cuts two lines. There are three pairs of lines here and angles may be "interior" or "corresponding" for one pair and not for another.

    If we label the top line "a", the middle line "b" and the bottom line "c", then angle 2 corresponds to angle 3 with respect to the pair "a" and "b". It corresponds to angle 10 with respect to pair "a" and "c". And angles 3 and 10 are corresponding with respect to pair "b" and "c".

    Oh, by the way, angles 1 and 6 are not "alternating" angles with respect to any pair. They are on the same side of transversal and "alternating" refers to being on opposite sides of the transversal.
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  3. #3
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    If we label the top line "a", the middle line "b" and the bottom line "c", then angle 2 corresponds to angle 3 with respect to the pair "a" and "b". It corresponds to angle 10 with respect to pair "a" and "c". And angles 3 and 10 are corresponding with respect to pair "b" and "c".
    Thanks for the response, my dear friend. With respect to the lines "a" & "b", how can angle 2 correspond to angle 3 when they are on the opposite side of the transversal? Same is the case with angle 2 & angle 10. With respect to the lines "a" & "c", how can angle 2 correspond to angle 10 when they are on the opposite side of the transversal? If I am not mistaken, corresponding angles lie on the same side of the transversal, don't they? Please correct me if I am wrong.

    Oh, by the way, angles 1 and 6 are not "alternating" angles with respect to any pair. They are on the same side of transversal and "alternating" refers to being on opposite sides of the transversal.
    Angles 1 & 6 are on the opposite side of the transversal...not on the same side....

    Thanks once again....
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