Transcript Congruence and Triangles

Congruence and Triangles
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The two triangle sides to the right
are congruent.
Theorem 4.3- Third Angles
Theorem- This states that if two
angles of one triangle are
congruent with two angles of
another triangle, then the third
angles are congruent.
Theorem 4.4- Properties of
Congruent Triangles- This states
that all congruent triangles are
either reflexive, symmetric or
transitive.
Because the two angles are
congruent the third angles of the
triangles to the right are
congruent.
Architects many times need to use
triangles such as in these buildings.
Proving Triangles are Congruent:
ASA and AAS
AAS Theorem- This
states that if two
angles and a
nonincluded side of
one triangle are
congruent to two
angles and the
corresponding
nonincluded side of a
second triangle, then
the two triangles are
congruent.
ASA Postulate- This
states that if two
angles and the
included side of one
triangle are congruent
to two angles and the
included side of a
second triangle, then
the two triangles are
congruent.
Jewelry designers often
use triangles in their
designs. They may need
to prove that they are
congruent in order to keep
it so that they do not look
weird on the wearer.
Isosceles, Equilateral, and Right
Triangles
This chapter shows that if two sides of
a triangle are congruent, then the
angles opposite them are congruent.
The converse of the above statement
is also true.
These statements are Theorems 4.6
and 4.7 in their respective orders.
Artists many times use all forms
of triangles in their art. This
example has all three forms of
angular triangles.