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4.2 Congruence and
Triangles
Essential Question: How can you
prove triangles congruent?
Congruent
Two figures are congruent if they
have the exact same size and shape.
 When two figures are congruent the
corresponding parts are congruent
(angles and sides).

Third Angles Theorem

If two angles of one triangle are
congruent to two angles of another
triangle, then the third angles are also
congruent.
Properties of Congruent Triangles

Congruence of triangles is reflexive,
symmetric, and transitive.
4.3 SSS and SAS

SSS: Side-Side-Side: If three sides of
one triangle are congruent to three of
a second triangle, then the two
triangles are congruent.

SAS: Side-Angle-Side: If two sides
and the included angle of one triangle
are congruent to two sides and the
included angle of a second triangle,
then two triangles are congruent.
4.4 ASA and AAS

ASA: Angle-Side-Angle: If two angles and the
included side of one triangle are congruent to
two angles and the included side of a second
triangle, then two triangles are congruent.

AAS: Angle-Angle-Side: If two angles and a
non-included side of one triangle are congruent
to two angles and the corresponding nonincluded side of a second triangle, then the two
triangles are congruent.
4.5 Using Congruent Triangles

CPCTC:

Corresponding Parts of Congruent Triangles are
Congruent: