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Congruent Triangles
Congruent Triangles – Triangles that are the
same size and same shape.
ABC is congruent to DEF, therefore:
A cong. to D
B cong. to E
C cong. to F
seg. AB cong. to seg. DE
seg. BC cong. to seg. EF
seg. AC cong. to seg. DF
Congruent Triangles
If all six of the corresponding parts of two triangles
are congruent, then the triangles are congruent.
Likewise, if two triangles are congruent, then all six
of the corresponding parts of the triangles are
congruent.
Corresponding Parts of Congruent Triangles are
Congruent (CPCTC) – Two triangles are
congruent if and only if their corresponding parts
are congruent.
The support beams on the fence form congruent
triangles.
a. Name the corresponding
congruent angles and sides of
ABC and DEF.
Answer:
b. Name the congruent triangles.
Answer: ABC DEF
Congruent Triangles
Theorem 4.4
• Congruence of triangles is reflexive, symmetric,
and transitive.
Reflexive: ABC is congruent to ABC
Symmetric: If ABC is congruent to DEF, then
DEF is congruent to ABC.
Transitive: If ABC is congruent to DEF and
DEF is congruent to GHI, then ABC is
congruent to GHI.
Congruent Triangles
Transformation – A redrawing of a figure in the
same plane such that each point of the image
corresponds to exactly one point of the original.
Congruence Transformations – Certain types of
transformations that preserve the size and shape of
the triangle.
• Slide (Translation), Flip (Reflection), Turn
(Rotation)
COORDINATE GEOMETRY The vertices of ABC are
A(–5, 5), B(0, 3), and C(–4, 1). The vertices of ABC
are A(5, –5), B(0, –3), and C(4, –1).
a. Verify that ABC ABC.
Answer:
Use a protractor to verify that
corresponding angles are
congruent.
b. Name the congruence transformation for ABC
and ABC.
Answer: turn