Complementary angles: Difference between revisions
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pair D = (0, 10), C = (10, 5), B = (10, 0), A = (0, 0); | pair D = (0, 10), C = (10, 5), B = (10, 0), A = (0, 0); | ||
draw(A--B); draw(C--A); draw(D--A); | draw(A--B); draw(C--A); draw(D--A); | ||
markscalefactor=0.1; | |||
draw(rightanglemark((0,10),(0,0),(10,0))); | |||
label("$A$", A, SW); | label("$A$", A, SW); | ||
label("$B$", B, SE); | label("$B$", B, SE); | ||
label("$C$", C, | label("$C$", C, NE); | ||
label("$D$", D, NE); | label("$D$", D, NE); | ||
</asy | </asy> | ||
As long as <math>\angle BAD</math> is a right angle, <math>\angle BAC</math> and <math>\angle CAD</math> are complementary angles to each other. | As long as <math>\angle BAD</math> is a right angle, <math>\angle BAC</math> and <math>\angle CAD</math> are complementary angles to each other. | ||
</center> | |||
== | ==Definitions== | ||
===Bing/Google=== | ===Bing/Google=== | ||
Either of two angles whose sum is | Either of two angles whose sum is <math>90^{\circ}</math> | ||
===Merriam-Webster=== | ===Merriam-Webster=== | ||
Two angles that add up to 90 degrees | Two angles that add up to <math>90</math> degrees | ||
==Properties and Examples== | |||
===Property=== | |||
<math>\angle A</math> is complementary to <math>\angle B</math> if and only if <math>\angle A + \angle B = 90</math> <math>\text{degrees}</math> | |||
===Examples=== | |||
If <math>\angle A</math> is <math>29</math> <math>\text{degrees}</math> and <math>\angle B</math> is <math>61</math> <math>\text{degrees}</math>, angle A and angle B are complementary since <math>29 + 61 = 90</math> | |||
If <math>\angle A</math> is <math>30</math> <math>\text{degrees}</math> and <math>\angle B</math> is <math>62</math> <math>\text{degrees}</math>, angle A and angle B are not complementary since <math>30 + 62 = 92</math>, and not <math>90</math> <math>\text{degrees}</math>. | |||
==Related Topics== | ==Related Topics== | ||
[[ | [[Complementary]] | ||
[[Angle]] | |||
[[ | {{stub}} | ||
[[Category:Definition]] | |||
[[Category:Geometry]] | |||
[[Category:Angles]] | |||
[[Category:Stubs]] | |||
Latest revision as of 07:57, 7 June 2023
Diagram
![[asy] import olympiad; size(150); pair D = (0, 10), C = (10, 5), B = (10, 0), A = (0, 0); draw(A--B); draw(C--A); draw(D--A); markscalefactor=0.1; draw(rightanglemark((0,10),(0,0),(10,0))); label("$A$", A, SW); label("$B$", B, SE); label("$C$", C, NE); label("$D$", D, NE); [/asy]](http://latex.artofproblemsolving.com/a/7/5/a75509ef276eae8b460d9b8cba0d1f1ad6b1b2ba.png)
As long as 
is a right angle, 
and 
are complementary angles to each other.
Definitions
Bing/Google
Either of two angles whose sum is 
Merriam-Webster
Two angles that add up to 
degrees
Properties and Examples
Property
is complementary to 
if and only if 
Examples
If is 
and is 
, angle A and angle B are complementary since 
If is 
and is 
, angle A and angle B are not complementary since 
, and not .
Related Topics
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