Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

give a counterexample?

if two angles are complimentary, then they must be adjacent?

4 Answers

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  • 1 decade ago
    Favorite Answer

    No, simply draw two angles, make one 60 and the other 30. They don't have to be in the same shape.

  • 1 decade ago

    Complimentary angles should be adjacent, otherwise they would not hear each other's compliments.

    Complementary angles (note the e instead of an i) are two angles that add up to 90 degrees.

    Draw an equilateral triangle (with the base horizontal, to make following the example easier).

    Draw a line from the top angle (A) falling perpendicularly at the mid-point of the base (D).

    You now have two identical right-angle triangles:

    ABD and ACD, where D is the right angle(s), B and C are 60 degrees each, and A is now two 30-degree angles.

    Take angle B from triangle ABD. (60 degrees)

    Take angle A from triangle ACD (30 degrees)

    They are not adjacent (they don't even belong to the same triangle) yet they add up to 90 degrees (they are complementary)

  • Anonymous
    1 decade ago

    Complimentary angles don't necessarily have to be in the same shape. This link explains complimentary angles pretty thoroughly:

    http://www.mathsisfun.com/geometry/complementary-a...

    Source(s): Life and College
  • Anonymous
    1 decade ago

    You can have two angles which are part of different polygonal figures but are still complementary. A counterexample demonstrating this might require a diagram of two complements in different figures.

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