LESSON 4-3:
TRIANGLE CONGRUENCE
By ASA AND AAS
Objective: Prove two triangles are congruent
using the ASA Postulate and AAS Theorem.
(NOTES…DNG page 77-79)
ASA (Angle-Side-Angle) Postulate
If two angles and an included side of one triangle are congruent to two angles and an
included side of another triangle, then the two triangles are congruent.
AAS (Angle-Angle-Side) Theorem
If two angles and a nonincluded side of one triangle are
congruent to two angles and a nonincluded side of
another triangle, then the two triangles are
congruent.
Theorem 4-1
Suppose that F is congruent to C and I is not congruent to C. Name the triangles
that are congruent by the ASA Postulate.
G
ASA
No; we need at least one more angle to prove congruence
by either the ASA Postulate or AAS Theorem.
Writing a Proof Using ASA
Write a paragraph proof.
Write a proof that uses AAS.
DCA
CDA
CA
AAS
Write a two-column proof that uses AAS.
Given
BAC ≅ DCA
alternate interior
Reflexive Property of Congruence
AAS Theorem
Write a proof.
4. Recall Example 4. Explain how you could prove ABC ≅ CDA using ASA.
It is given that AB CD . Thus, BAC ≅ DCA by the Alternate Interior s Theorem.
It is also given that B ≅ D. Thus, BCA ≅ DAC by Theorem 4-1.
AC
 CA
by the Reflexive Property of ≅.Therefore, ABC ≅ CDA by ASA.
Practice 4-3
Triangle Congruence by ASA & AAS
Tell whether the ASA Postulate or the AAS Theorem can be applied directly to prove the
triangles congruent. If the triangles cannot be proved congruent, write not possible.
not possible
ASA Postulate
AAS Theorem
not possible
AAS Theorem
not possible
Practice 4-3
Triangle Congruence by ASA & AAS
Tell whether the ASA Postulate or the AAS Theorem can be applied directly to prove the
triangles congruent. If the triangles cannot be proved congruent, write not possible.
AAS Theorem
ASA Postulate
not possible
Statements
Reasons
1. Given
2. Vertical s Theorem
3. ASA Postulate
Practice 4-3
Triangle Congruence by ASA & AAS
Practice 4-3
Triangle Congruence by ASA & AAS
What else must you know to prove the triangles congruent for the reason shown?
((
G
or
H