Download Section 4.4 Day 1 Proving Triangles are Congruent ASA and AAS

Week 4
11.09.11
Warm Up
Describe what each acronym means:
1) AAA
2) AAS
3) SSA
4) ASA
Geometry
4.4 Day 1
I will prove that triangles are congruent using
the ASA and AAS Postulates.
Postulate
21
ASA - Angle Side Angle Congruence
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 triangles are congruent.
B
E
C
A
∠A ≅ ∠D
F
D
≅
∠C ≅ ∠F
∆ABC ≅ ∆DEF because of ASA.
Theorem
4.5
AAS - Angle Angle Side Congruence
If two angles and a non-included side of one triangle
are congruent to two angles and the corresponding
non-included side of a second triangle, then the two
triangles are congruent.
B
E
C
A
If
∠A ≅ ∠D ,
then
D
≅
F
, and ∠C ≅ ∠F
∆ABC ≅ ∆DEF because of AAS.
Ex 1
Prove Theorem 4.5: ∆ABC ≅ ∆DEF:
B
E
C
A
Statement
F
D
Reason
∠A ≅ ∠D
Given
∠C ≅ ∠F
Given
≅
Given
∠B ≅ ∠E
∆ABC ≅ ∆DEF
Third Angle Theorem (4.3)
ASA ( P21 )
Ex 2
Prove ∆EFG ≅ ∆JHG:
E
H
G
F
≅
J
is given.
∠E ≅ ∠J
is given
∠EGF ≅ ∠JGH
are vertical angles.
∆EFG ≅ ∆JHG
because of AAS.
Ex 3
Prove ∆ABD ≅ ∆EBC:
C
A
B
D
Statement
E
Reason
≅
Given
∥
Given
∠D ≅ ∠C
∠ABD ≅ ∠EBC
∆ABD ≅ ∆EBC
Alternate Interior Angles
Theorem (3.8)
Vertical Angles Theorem (2.6)
ASA
Do: 1
Is ∆NQM ≅ ∆PMQ?
statements to prove it.
Give congruency
Q
N
M
Assignment:
P
Textbook Page 223, 8 - 22 all.