Download Fired Up about Section 7.2

Two Proof Oriented Triangle Theorems
Richuan Hu
Section 8
Honors Geometry
Mr. Pricci
Now douse it and learn
 As the section name implies, there is two theorems
that are often used in proofs about triangles in this
section.
 The two theorems are the No – Choice Theorem and
the AAS Theorem.
The No Choice theorem states that…
 If two angles of one triangle are congruent to two
angles of a second triangle, then the third angles are
congruent.


3
C
A
1
2
B
Do You have A Choice?
 No, you don’t, suck it up, you’ll live.
 Because if two angles of two triangles are the same, no
matter how the sides differ, the third angle is going to
be the same.
Proof that you don’t have a choice
 It is a truth universally acknowledged, that any triangle
big or small always has a sum of 180 degrees.
 If  1   A, 2   B
 By subtraction, angle 3 and angle C must be congruent
3
C
1
2
A
B
Exemplifying your lack of choice
 Pg 321 #11)Find m  3in diagram as marked.

Since the two triangles are right triangles, the
right angles are congruent. Because the big
triangle is isosceles as given, the 70 degree angle
is congruent to the corresponding one on the
other side. Therefore, angle 3 is congruent to the
adjacent angle by no choice. Angle 3 is 20
degrees from 180 – 90 – 70.
3
70 °
C
R
Pg 303 Sample Problems #1
Given:
R   C
Prove:
H 
U
I
H
U
Answers
 Pg 303 #1
S
1)  R   C
2)  ABE   DBC
3)H   U
R
1) Given
2) Vertical angles are congruent
3) No Choice Theorem
The AAS StAteS that…
 If there exist a correspondence between the vertices of
two triangles such that two angles and a nonincluded
side of one are congruent to the corresponding parts of
the other, then the triangles are congruent.
 In English
If two angles and a side not in between them of two triangles
are congruent, the two triangles are congruent.
Proof of AAS
S
1) C  F
2)  A   E
3)  B   E
4)
ABC 
DEF
R
1)
2)
3)
4)
Given
Given
No Choice Theorem
ASA (1,2,3)
Givens:

The AAS is usually associated with…
 Theorems that prove triangles congruent, like the SSS,
ASA, and SAS.
Works Cited
 Geometry for Enjoyment and Challenge, McDougal & Company, Evanston, Illinois, 1997.
 Austen, Jane. Pride and Prejudice, Penguin Books, New York,2006.
 http://www.mathwarehouse.com/geometry/congruent_triangles/angle-angle-sidepostulate.php