Download AAS Theorem - Math Story

Aim: How do we prove triangles congruent using the
Angle-Angle-Side Theorem?
Do Now: In each case, which postulate can be used
to prove the triangles congruent?
1)
2)
3)
S.A.S.
S.S.S.
4)
A.S.A.
A.A.S. Theorem
Theorem #20: Angle-Angle-Side Theorem (A.A.S.)
If
two angles and the non-included side are congruent to two
angles and the corresponding non-included side of another
triangle, the two triangles are congruent.
1
Ex: A.A.S Theorem
In each case, state whether A.A.S. be used to prove the
triangles congruent.
2)
1)

3)
X

Geometry Lesson: Angle-Angle-Side
Theorem
2
Ex: A.A.S. Theorem
Given: RG  MT
M  T
Prove: MG  TG
R
M
G
Statement
Reason
1) RG  MT
2) MGR, TGR are rt. 's
3) MGR  TGR
4) M  T
5) RG  RG
6) MGR  TGR
7) MG  TG
T
1) Given
2) Def. perpendicular lines
3) Right 's are congruent.
4) Given
5) Reflexive Postulate
6) A.A.S. Theorem
7) C.P.C.T.C.
Geometry Lesson: Angle-Angle-Side
Theorem
3
P
Ex: 1,2,3 A.A.S. Theorem:
R
1) Given: BP bisects RPM
R  M
Prove: PRB  PMB
M
B
2) Given: Isosceles DES with SD  SE
ET  DS , DR  ES
Prove: ET  DR
S
T
D
3) Given: MPV bisects HPK
H  K
Prove: MP  VP
R
E
H
P
V
M
Geometry Lesson: Angle-Angle-Side
Theorem
K
4
Ex: 4, 5 A.A.S. Theorem:
4) In ABC and EFG, mA  42, mB  68,
CA  12 cm, mF  42, mG  68, and EF  12 cm.
Is ABC  FGE? Explain.
5) In ABC and EFG, mA  50, AB  20, BC  16,
mE  50, EF  20, and FG  12.
Is ABC  EFG? Explain.
Geometry Lesson: Angle-Angle-Side
Theorem
5