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 angle and the two sides next to the angle must be proportional.
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===AoPS===
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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.
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===Mathwords Definition===
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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.
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==Diagram==
 
==Diagram==
 
<asy>
 
<asy>
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</asy>
 
</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.
 
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.
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==See Also==
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*[[Similarity]]
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*[[Congruence]]
  
 
==Categories==
 
==Categories==
  
 
[[Category:Geometry]] [[Category:Mathematics]][[Category:Stubs]]
 
[[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

[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 $m\angle CAB = m\angle FDE$ and $\dfrac{CA}{FD} = \dfrac{AB}{DE}$, then the triangles are similar by SAS similarity.

See Also

Categories

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