CK12 - Geometry

Example 1

Whatinformationwouldyou needto provethat thesetwo triangleswerecongruentusingthe SAS postulate?

A. the measuresof and

B. the measuresof and

C. the measuresof and

D. the measuresof sides and

If you are to use the SAS postulateto establishcongruence,you needto havethe measuresof two sides
and the anglein betweenthemfor both triangles.So far, you haveone side and one angle.So, you must

use the otherside adjacentto the sameangle.In , that side is. In triangle , the

correspondingside is. So, the correctansweris C.

AAAand SSA relationships

You havelearnedso manydifferentwaysto provecongruencebetweentwo triangles,it may be tempting
to thinkthat if you haveany pairsof congruentthreeelements(combiningsidesor angles),you can prove
trianglecongruence.

However, you may havealreadyguessedthat AAA congruencedoesnot work.Evenif all of the anglesare
equalbetweentwo triangles,the trianglesmay be of differentscales.So, AAA can only provesimilarity,
not congruence.