1. 7-3: Exterior Angle Inequality Theorem
Proof Geometry

2. 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.

3. Exterior Angle formal Defintion
If C is between A and D, then BCD is an exterior angle of ABC

4. Every triangle has 6 exterior angles.2 1 3 X 4 6 5 X
X = not exterior angles

5. 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

6. Exterior Angle inequality Theorem
Given: ABC with C between A and D
Prove: BCD > B
Introduce E, the midpoint of Midpoint Theorem
On the ray introduce Point plotting Theorem point F so that EF = EA
Introduce Line Postulate

7. Exterior Angle inequality Theorem
Given: ABC with C between A and D
Prove: BCD > B
BEA  CEF Vertical Angle Theorem
BE = EC Def. of midpoint
BEA  CEF SAS
B  ECF CPCTC
BCD > ECF Parts Theorem
BCD > B Transitive prop of ineq.

8. Corollary Exterior Angle Inequality
If a triangle has one right angle, then its other angles are acute.

9. Corollary Exterior Angle Inequality
If a triangle has one right angle, then its other angles are acute. You try!

10. Given: The figure Prove: ∠A<∠𝐷𝐸𝐹
You Try!
DEF > B Ext.  Ineq. Theorem
B > A Ext.  Ineq. Theorem
DEF > A Transitive prop. of ineq.

11. Homework
pg : #1-10