Download Exterior Angle inequality Theorem - Andrew Busch

7-3: EXTERIOR ANGLE
INEQUALITY THEOREM
PROOF GEOMETRY
EXTERIOR ANGLE OF A TRIANGLE
• 3 is called an exterior
angle of the triangle
• An exterior angle is
created by lengthening
one of the sides of the
triangle.
• An exterior angle forms
a linear pair with one
of the angles of the triangle.
• The other two angles of the triangle are called the
remote interior angles.
EXTERIOR ANGLE FORMAL DEFINTION
• If C is between A and D, then BCD is an exterior
angle of ABC
Every triangle has 6 exterior angles.
X
1
2
3
X
4
6
X
5
X = not exterior angles
EXTERIOR ANGLE INEQUALITY
THEOREM
An exterior angle of a triangle is greater than
each of its remote interior angles
Given ABC. If C is
between A and D, then
BCD > B
EXTERIOR ANGLE INEQUALITY
THEOREM
Given: ABC with C between A and D
Prove: BCD > B
1. Introduce E, the midpoint of BC
2. On the ray AE introduce
point F so that EF = EA
3. Introduce FC
Midpoint Theorem
Point plotting Theorem
Line Postulate
EXTERIOR ANGLE INEQUALITY
THEOREM
Given: ABC with C between A and D
Prove: BCD > B
1.
2.
3.
4.
5.
6.
BEA  CEF
BE = EC
BEA  CEF
B  ECF
BCD > ECF
BCD > B
Vertical Angle Theorem
Def. of midpoint
SAS
CPCTC
Parts Theorem
Transitive prop of ineq.
COROLLARY EXTERIOR ANGLE
INEQUALITY
If a triangle has one right angle, then its other
angles are acute.
COROLLARY EXTERIOR ANGLE
INEQUALITY
If a triangle has one right angle, then its other
angles are acute.
You try!
Given: The figure
Prove: ∠A < ∠𝐷𝐸𝐹
You Try!
1. DEF > B
2. B > A
3. DEF > A
Ext.  Ineq. Theorem
Ext.  Ineq. Theorem
Transitive prop. of ineq.
HOMEWORK
pg. 219-220: #1-10