Honors Geometry Section 4.3
AAS / RHL
In the last section we learned of three
triangle congruence postulates:
SSS
SAS
ASA
Let’s look at some other
possibilities.
A counterexample demonstrates that AAA
is not a valid test for congruence. Consider
two equiangular triangles. What is true
about the angles in each triangle?
They are all 60 degrees.
Are the triangles shown congruent?
No
50
50
If we know the measures of two angles
in a triangle, we will always be able to
find the measure of the third angle.
So, any time we have the AAS
combination, we can change it into the
ASA combination and the two triangles
will then be congruent.
Theorem 4.3.1 AAS (Angle-Angle-Side) Congruence Theorem
If two angles and the non-included side of
one triangle are congruent to the
corresponding parts of another
triangle, then the triangles are congruent.
Note: While ASA can be used
anytime AAS can be used and viceversa, they are different. The
congruence markings on your
triangles and the steps in your
proof must agree with the
congruence postulate/theorem
you use.
Example: Are the triangles congruent,
and if so, why?
AAS
ASA
As discussed in the last class, SSA is
not a valid test for triangle
congruence.
There is, however, a special case of
SSA that is a valid test for triangle
congruence.
Theorem 4.3.2 RHL (Right-HypotenuseLeg) Congruence Theorem
If the hypotenuse and a leg of one
right triangle are congruent to the
hypotenuse and a leg of a second right
triangle, then the two triangles are
congruent.
NOTE: In a right triangle, the legs
are the two sides that form the
right angle and the hypotenuse is
the side opposite the right angle.
Example 3: Name the congruent triangles and
give the reason for their congruence. None is a
possible answer.
AAS or ASA
RHL
 CAL   CAF
NONE
 KEN   FEI