Download Congruent Triangles - Hudson Falls Middle School

By, Alyssa Fountaine
Sarah Dimick
Spencer Mercure
Angle-Side-Angle (ASA)
 If two angles and the included side of a
triangle are congruent to two angles and the
included side of another triangle, then the
tw0 triangles are congruent.
Side-Side-Side (SSS)
 If three sides of a triangle are congruent to
three sides of another triangle, then the two
triangles are congruent.
Angle-Angle-Side (AAS)
 If two angles and a nonincluded side of one
triangle are congruent to two angles and the
corresponding nonincluded side of another
triangle, then the two triangles are
congruent.
Side-Angle-Side (SAS)
 If two sides and the included angle of a triangle
are congruent to two sides and the included
angle of another triangle then the triangles are
congruent.
Hypotenuse-Leg(HL)
 If the
hypotenuse
and a leg of
one right
triangle are
congruent to
the
hypotenuse
and a leg of
another right
triangle, then the triangles are congruent.
CPCTC
 CPCTC:
Congruent Parts of Congruent Triangles are Congruent
 Once you know that two triangles are congruent, you
can make conclusions about corresponding segments
and angles because of CPCTC.
Donkey Theorem and AAA
 “No Swearing in math class forwards or backwards.”
 Angle-Side-Side and Side-Side-Angle cannot be used
to prove congruency because it cannot guarantee that
one unique triangle will be drawn.
 Angle-Angle-Angle(AAA) cannot be used to prove
congruency because two triangles can have the same
angle but different side measures. They would be
similar.
Isosceles Triangle Theorem
 If two sides of a triangle are congruent, then the angles
opposite those sides are congruent.
 Converse: If two angles of a triangle are congruent,
then the sides opposite the angles are congruent.
Corollary
 If a triangle is equilateral, then the triangle is
equiangular.
 <X = <Y =<Z
 If a triangle is equiangular, then the triangle is
equilateral.
 XY=YZ=ZX