Transcript AAS Theorem
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, mA 42, mB 68,
CA 12 cm, mF 42, mG 68, and EF 12 cm.
Is ABC FGE? Explain.
5) In ABC and EFG , mA 50, AB 20, BC 16,
mE 50, EF 20, and FG 12.
Is ABC EFG? Explain.
Geometry Lesson: Angle-Angle-Side
Theorem
5