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Geometry
Name:
Period:
Date:
Warm Up 1/23
Lesson 4-5: Triangle Congruence: ASA, AAS, and HL
Objectives
Students will…
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Be able to define the Angle-Side-Angle Congruence, Angle-Angle-Side Congruence Postulate, and
Hypotenuse-Leg Postulate.
Be able to prove triangle congruence using ASA, AAS, and HL Congruence Postulate.
Proving Congruent Triangles
Now, if we use the definitions of congruent triangles to prove that two or more triangles are congruent, we would
have to show each corresponding side and angle pairs (___ total) are congruent. This could take a lot of space and
time! Luckily, we have some shortcuts we can take. These are known as the _______________________________
________________.
Angle-Side-Angle (ASA) Congruence
Contrary (and yet somewhat similar) to SAS postulate, if we are given two __________, along with an __________
__________, we can use the _________________________________Congruence Postulate.
Angle-Side-Angle Congruence (SSS)- 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.
Ex.
Angle-Angle-Side (AAS) Congruence
We can have another postulate involving two angles and one side. The ________________________ Postulate,
involves two angles and a __________________side.
Angle-Angle-Side Congruence (AAS)- If two angles and a non-included side of one triangle are congruent to the
corresponding angles and non-included side of another triangle, then the triangles are congruent.
Ex.
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Geometry
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Period:
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ASA vs AAS
Similar to the included angle in the SAS postulate, ASA calls for the lone side to be the included side. The included
side can also be understood as the side that “______________” the two angles. Again, if we have a non-included
side, we have the case of AAS.
VS
Hypotenuse-Leg Postulate
th
In regards to triangle congruence, there exists a possible 5 postulate, known as _________________Postulate
(HL). We say that this postulate “possibly” exists, because it only works in a special case: _____________________
___________________.
Hypotenuse-Leg Postulate- If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a
leg of another right triangle, then the triangles are congruent.
Ex.
Example
State if the two triangles are congruent. If they are, state how you know.
Homework 1/23
ASA, AAS, and HL Worksheet
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