Download Triangle Congruence - Mr. Beals Quest

TRIANGLE
CONGRUENCE
Congruence Definition:
• Two triangles are congruent if
corresponding sides are congruent
AND corresponding angles are
congruent.
Side-Side-Side (SSS) Postulate
• If the sides of one triangle are
congruent to the sides of a second
triangle, then the triangles are
congruent.
Example: Prove ΔABC≅ΔDBC
• Given: AB=DB & C is
midpoint of AD.
• AB=DB………Given
• AC=DC…Midpoint Def
• BC=BC…Identity
• ΔABC≅ΔDBC…SSS
Side-Angle-Side (SAS) Postulate
• If two sides and the included angle
of one triangle are congruent to
two sides and the included angle
of another triangle, then the
triangles are congruent.
Example: Prove ΔABE≅ΔCBD
• Given: AB=DB,
EB=CB
• AB=DB…Given
• EB=CB…Given
• ∠ABE=∠CBD…Vertic
al angles
• ΔABE≅ΔCBD…SAS
Angle-Side-Angle (ASA) Postulate
• If two angles and the included side
of one triangle are congruent to
two angles and the included side
of another triangle, then the
triangles are congruent.
Example: Prove ΔABC≅ΔCDA
• Given: AB || CD
• ∠ABC = ∠CDA
• ∠ABC = ∠CDA…Given
• ∠BAC = ∠ACD…Alt.Int.
angles are congr.
• AC=AC = Identity(reflexive)
• ΔABC≅ΔCDA…AAS
Angle-Angle-Side (AAS) Postulate
• If two angles and a non-included
side of one triangle are congruent
to the corresponding two angles
and side of a second triangle, then
the two triangles are congruent.
Example: Prove ΔSRT≅ΔURT
• ∠RST = ∠RUT…
• Given
• ∠STR = ∠UTR…
• Given
• RT=RT…Identity(Reflexive)
• ΔSRT≅ΔURT…AAS
Practice