Download Unit 4.4

UNIT 4: CONGRUENT TRIANGLES
4.4 – Proving Triangles are Congruent: ASA and AAS
MA30: GEOMETRY
(Text Ref: Ch 4.4 Pg 220-227)
Using the
ASA & AAS
Congruence
Methods
I. Using the ASA and AAS Congruence Methods
A. Identifying the Included Side
1) Definition of Included Side
Define & Identify
Included Side
2) Identify the Included Side of the Triangles.
(a)
Postulate 21
Angle-Side-Angle
Congruence
Postulate
Determine if
ASA Congruence
Postulate
Applies
Theorem 4.5
Angle-Angle-Side
Congruence
Theorem
(b)
(c)
B. Postulate 21 – Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are congruent to two
angles and the included side of a second triangle, then the two triangles are
congruent.
C. Determine whether the ASA Congruence Postulate can be used to
prove the triangles are congruent. Explain.
1)
2)
3)
D. Theorem 4.5 – Angle-Angle-Side Congruence Theorem
If two angles and a nonincluded side of one triangle are congruent to two
angles and the corresponding nonincluded side of a second triangle, then
the two triangles are congruent.
4.4 – Proving Triangles are Congruent: ASA and AAS (continued)
Showing Triangles
are Congruent
Identifying Needed
Congruences.
E. Showing Triangles are Congruent
Does the diagram give enough information to show that the triangles are
congruent? If so, state the postulate or theorem you would use. Explain.
1)
2)
Marking Tip
3)
4)
Marking Tip
5)
6)
Marking Tip
F. State the third congruence that must be given to prove the two
triangles are congruent using the indicated postulate or theorem.
1) ASA Congruence Postulate
2) AAS Congruence Theorem
3) ASA Congruence Postulate
4) AAS Congruence Theorem