Download 7.2 Two Proof-Oriented Triangle Theorems Example:

7.2 Two Proof-Oriented Triangle Theorems
Your book refers to the following as the NO-CHOICE Theorem.
Theorem 53: If two angles of one triangle are congruent to two angles of a 2nd triangle, then the 3rd angles are
congruent. (No- Choice Theorem)
Example 1: (recall Theorem 50!)
(duh!)
30⁰
(duh!)
120⁰
30⁰
120⁰
NOTE: The two triangles DO NOT have to be congruent in order to apply the “No-Choice” Theorem
Example 2:
A
Given:
O
C
T
C
T
Conclusion:
A
D
D
G
O
G
Theorem 54: (AAS) If two angles and a non- included side of one triangle are congruent to the
corresponding two angles and non- included side of a second triangle then the triangles are congruent.
This theorem makes some of the earlier, impossible to prove congruence problems – possible to prove!
D
C
Example:
Given:
ABCD is a Rhombus
AF CB
CE AB
F
Prove:
1
2
3
4
5
6
7
CE AF
ABCD is a Rhombus
CB AB
AF CB, CE AB
∡ CEB ∡ AFB
∡B ∡B
Δ CEB Δ AFB
CE AF
A
(S)
(A)
(A)
1
2
3
4
5
6
7
E
Given
In a rhombus, all sides are
Given
segs form right ∡s
Reflexive Property
AAS (4, 5, 2)
CPCTC
B