From Latin: complementum - "that which fills up or completes"
Definition: Two angles that add up to 90°
Try this Drag an orange dot. The two angles will change so that they always add to 90°
In the figure above, the two angles ∠PQR and
∠JKL are complementary because they always add to 90°
Often the two angles are
adjacent, in which case they form a
right triangle, the two smaller angles are always complementary.
(Why? - one angle is 90° and all three add up to 180°.
Therefore the two smaller ones must add to 90° and so are complementary by definition).
See the page on right triangles
and convince yourself that this is true.
Similar in concept are supplementary angles, which add up to 180°.
A way to remember
Sometimes it's hard to remember which is which between supplementary (adds to 180°) and complementary (adds to 90°). Here are two memory aids:
- The phrase "it's right to give compliments" A right angle is 90 degrees and, yes, 'compliment' and 'complement' are not the same word, but it's a way to remember which is which.
Put a vertical line on the right of the letter 'c' in 'complementary' to make into a '9'. Complementary angles add to 90.
Other angle topics
(C) 2009 Copyright Math Open Reference. All rights reserved