Difference between revisions of "Complementary angles"
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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> | ||
| Line 13: | Line 15: | ||
</center> | </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== | ==Properties and Examples== | ||
===Property=== | ===Property=== | ||
| − | <math>\angle A</math> is complementary to <math>\angle B</math> if and only if <math>\angle A + \angle B = | + | <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=== | ===Examples=== | ||
| − | If <math>\angle A</math> is <math>29</math> <math>degrees</math> and <math>\angle B</math> is <math>61</math> <math>degrees</math>, angle A and angle B are complementary since <math>29 + 61 = 90</math> | + | 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>degrees</math> and <math>\angle B</math> is <math>62</math> <math>degrees</math>, angle A and angle B are not complementary since <math>30 + 62 = 92</math>, and not <math>90</math> degrees. | + | 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]] | [[Angle]] | ||
| + | |||
| + | |||
{{stub}} | {{stub}} | ||
| Line 39: | Line 43: | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
[[Category:Angles]] | [[Category:Angles]] | ||
| + | [[Category:Stubs]] | ||
Latest revision as of 07:57, 7 June 2023
Contents
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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