# Difference between revisions of "SAS Similarity"

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==Definition== | ==Definition== | ||

− | SAS stands for Side-Angle-Side, for two [[triangle]]s to be [[similar|similar triangles]] by SAS similarity, they must have a pair of congruent | + | ===AoPS=== |

+ | SAS stands for Side-Angle-Side, for two [[triangle]]s to be [[similar|similar triangles]] by SAS similarity, they must have a pair of congruent angles and the two sides next to the angle must be proportional. | ||

+ | |||

+ | ===Mathwords Definition=== | ||

+ | Side-angle-side similarity. When two triangles have corresponding angles that are congruent and corresponding sides with identical ratios as shown below, the triangles are similar. | ||

+ | |||

+ | ==Diagram== | ||

+ | <asy> | ||

+ | dot((0,0)); | ||

+ | label("A",(0,0),SW); | ||

+ | dot((5,0)); | ||

+ | label("B",(5,0),SE); | ||

+ | dot((3,4)); | ||

+ | label("C",(3,4),N); | ||

+ | draw((0,0)--(5,0)--(3,4)--cycle); | ||

+ | markscalefactor = 0.1; | ||

+ | draw(anglemark((5,0),(0,0),(3,4))); | ||

+ | </asy> | ||

+ | <asy> | ||

+ | size((8cm)); | ||

+ | dot((0,0)); | ||

+ | label("D",(0,0),SW); | ||

+ | dot((5,0)); | ||

+ | label("E",(5,0),SE); | ||

+ | dot((3,4)); | ||

+ | label("F",(3,4),N); | ||

+ | draw((0,0)--(5,0)--(3,4)--cycle); | ||

+ | markscalefactor = 0.0675; | ||

+ | draw(anglemark((5,0),(0,0),(3,4))); | ||

+ | </asy> | ||

+ | If <math>m\angle CAB = m\angle FDE</math> and <math>\dfrac{CA}{FD} = \dfrac{AB}{DE}</math>, then the triangles are similar by SAS similarity. | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Similarity]] | ||

+ | *[[Congruence]] | ||

+ | |||

==Categories== | ==Categories== | ||

− | + | ||

− | + | [[Category:Geometry]] [[Category:Mathematics]][[Category:Stubs]] |

## Latest revision as of 21:12, 28 January 2021

## Definition

### AoPS

SAS stands for Side-Angle-Side, for two triangles to be similar triangles by SAS similarity, they must have a pair of congruent angles and the two sides next to the angle must be proportional.

### Mathwords Definition

Side-angle-side similarity. When two triangles have corresponding angles that are congruent and corresponding sides with identical ratios as shown below, the triangles are similar.

## Diagram

If and , then the triangles are similar by SAS similarity.