Download Congruent Triangles (Notes from class)

Investigating Triangles
Congruent triangles: two triangles are congruent if
their corresponding parts are congruent.
SSS (Part 1 Triangle)
Side-Side-Side Congruence Postulate
If three sides of one triangle are congruent to three
sides of a second triangle, then the triangles are
congruent.
SAS (Part 2 Triangle)
Side-Angle-Side Congruence Postulate
If two sides and the included angle of one triangle
are congruent to two sides and an included angle
of another triangle, then the triangles are
congruent.
ASA, (Part 3 Triangle)
Angle-Side-Angle Congruence Postulate
If two angles and the included side of one triangle
are congruent to two angles and the included side
of another triangle, the triangles are congruent.
AAS (Part 4 Triangle)
Angle-Angle-Side Congruence 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, the two
triangles are congruent.
AAA (Part 5 Triangle)
Angle-Angle-Angle
Many different triangles can be constructed when
given three angles.
ASS or SSA (Demonstrated with straws and pin.)
More than one triangle can have two sides and one
angle in common if the angle is not included
between the sides (SAS).
Application: Is it always necessary to show that all
of the corresponding parts of two triangles are
congruent to be sure that the two triangles are
congruent?
For example, if you are designing supports for the
beams in a roof, must you measure all three sides
and all three angles to ensure that the supports
are identical?
Or is checking 3 measurements enough to ensure
that all braces will be identical? You can use
congruent triangles to solve many real-life
problems such as those found in designing and
constructing buildings and bridges.
Homework:
Draw pairs of congruent triangles to represent the
four congruence postulates. Label each heading (SSS,
ASA, SAS, AAS) and use appropriate tick marks to
identify congruent parts.