Download Sections 4

Introduction to Sections 4-3 thru 4-5
“Triangle Congruence Shortcuts”
Objective:
To learn about 5 shortcut methods we can use to prove
that 2 triangles are congruent to each other.
Background:
We previously learned that to prove that two triangles
were congruent to each other, we would have to prove
that all of the angles (3) and sides (3) of both triangles
were congruent to each other.
Now, instead of having to check that all 3 pairs of
corresponding sides and all 3 pairs of corresponding
angles are congruent, we can use any one of the following
shortcuts to prove that two triangles are congruent.
1)
SSS Postulate (Side-Side-Side)
“If the three sides of one triangle are congruent
to the 3 corresponding sides of another triangle,
then the triangles are congruent.”
2)
SAS Postulate (Side-Angle-Side)
“If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.”
3)
ASA Postulate (Angle-Side-Angle)
“If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, then the
triangles are congruent.”
4)
5)
AAS Postulate (Angle-Angle-Side)
“If two consecutive angles followed by a side of a
triangle are congruent to two consecutive angles
followed by a side of another triangle, then the
triangles are congruent.”
HL Theorem (Hypotenuse-Leg)
Note: Only used with Right Triangles
“If the hypotenuse and leg of a right triangle
are congruent to the hypotenuse and leg of
another right triangle, then the triangles are
congruent.”
Note:
AAA (Angle-Angle-Angle) and SSA (Side-Side-Angle) do
not prove that two triangles are congruent to each other.