Download Triangle Congruence Theorems

Triangle Congruence Theorems
Geometry Notes – 4.2/4.3
Mr. Belanger
Importance
• Used to prove triangles congruent
• Gives many options for proving
congruence
• Will continue to be used following this
chapter
SSS Congruence Theorem
Side – Side – Side Congruence: If three
corresponding sides in two triangles are
congruent, then the triangles are congruent.
SAS Congruence Theorem
Side – Angle – Side Congruence: If, in two
triangles, two sides and the included angle
(formed by the two sides) are congruent, then
the triangles are congruent.
ASA Congruence Theorem
Angle – Side – Angle Congruence: If, in
two triangles, two angles and the side
connecting them are congruent, then the
triangles are congruent.
AAS Congruence Theorem
Angle – Angle – Side Congruence: If, in two
triangles, two angles and the non-included (not
between) side are congruent, then the triangles
are congruent.
Examples:
Try to decide if the triangles are
congruent and if so, why?
SAS
Examples:
Try to decide if the triangles are
congruent and if so, why? NO! AAA not a
congruence theorem
Examples:
In triangle ADB and ADC, angle A is
congruent to both, side AD is
congruent to both and sides BD = CD.
It’s obvious that
ADB and ADC are
not congruent. Be
careful about just
matching up any
three parts like SSA.
It has to be one of
the four theorems.
Examples:
Are the triangles congruent?
Yes, AAS
Now memorize these four
theorems!