Transcript Week 13 - Troy High School

Week 13
5.6 – Indirect Proof and
Inequalities in Two Triangles
Hinge Theorem  If two sides one triangle are
congruent to two sides of another triangle, but the
included angle of the first triangle is larger than the
included angle of the second, then the third side of
the first triangle is longer than the third side of the
second triangle.
Fancy talk for two sides same, one angle bigger than
other, then side is bigger
Given : BA  ED, BC  EF,
D
A
mB  mE
T hen: AC  DF
E
B
C
F
Converse of Hinge Theorem  If two sides one
triangle are congruent to two sides of another
triangle, but the 3rd side of the first triangle is longer
than the 3rd side of the second, then the included
angle of the first triangle is larger than the included
angle of the second.
Fancy talk for two sides same, one sidee bigger than
other, then angle is bigger
Given : BA  ED, BC  EF,
D
A
AC  DF
T hen: mB  mE
E
B
C
F
List the angles and sides in order
S
S
U
30o
D
U
35o
2
1
14
45o
D
C
13
70o
70o C
K
K
____ < ____ < ____
____ < ____
____ < ____ < ____
____ < ____
student
Indirect Proof
How to write an indirect proof
1. Assume temporarily that the conclusion is
not true.
2. Reason logically until you reach a
contradiction of the known fact.
3. Point out the temporary assumption is
false, so the conclusion must be true.
Practice  Write the untrue
conclusion
Prove : n is odd
Prove: sum of interior
angles of a triangleis 180
Prove: AB  AB
Prove: Mr. Kim is a genius
a
b
1
3
Given : m1  m3
Prove: a || b
Given : m1  50, m2  60
Prove: 1 and 2 are not a linear pair
a
b
Given : 1, 3 not supp.
1
3
Prove: a || b