AAS Congruence

Pronunciation: /eɪ eɪ es kən'gru əns/ Explain

Manipulative 1 - Triangles that are congruent by AAS.

Two triangles are congruent if two adjacent angles and a side of one triangle are congruent with corresponding angles are congruent with two angles of the other triangle and a side that is not between the two angles is congruent with a corresponding side of the other triangle.[1] In this case we say that the triangles are AAS congruent. AAS stands for Angle, Angle, Side.

Click on the blue points in the manipulatives and drag them to change the figures.

Proof of AAS Congruence
StepManipulativeClaimDiscussion
1
Angle A is congruent with angle A'. These are the criterion for the proof. These are assumed to be true.
Angle B is congruent with angle B'.
Line segment BC is congruent with line segment B'C'.
2 To show:
Triangle ABC is congruent with triangle A'B'C'.
This is the claim. The proof will show that the claim is true.
3
If
Angle A is congruent with angle A'.
and
Angle B is congruent with angle B'.
then
Angle C is congruent with angle C'
If two corresponding angles of two triangles are congruent, then the third angle is congruent.
4
Since
Angle B is congruent with angle B'.
and
Angle C is congruent with angle C'
and
Line segment BC is congruent with line segment B'C'.,
then
Triangle ABC is congruent with triangle A'B'C'.. Q.E.D.
Use ASA congruence to show that the two triangles are congruent.

References

  1. Euclid. Elements Book 1 Proposition 26. D. Joyce. 3/12/2009. http://cs.clarku.edu/~djoyce/java/elements/bookI/propI26.html.
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Cite this article as:


AAS Congruence. 6/12/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/aascongruence.html.

Image Credits

Revision History


5/8/2018: Removed broken links, updated Geogebra apps, updated license. (McAdams, David E.)
1/4/2010: Added "References". (McAdams, David E.)
11/25/2008: Changed equations to images. (McAdams, David E.)
10/5/2008: Added proof. (McAdams, David E.)
9/16/2008: Repaired GeoGebra drawing to eliminate disappearing lines and reflex angles. (McAdams, David E.)
8/25/2007: Changed figure 1 from image to manipulative. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)


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