Presentation is loading. Please wait.

Presentation is loading. Please wait.

7-3: Exterior Angle Inequality Theorem

Similar presentations


Presentation on theme: "7-3: Exterior Angle Inequality Theorem"— Presentation transcript:

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


Download ppt "7-3: Exterior Angle Inequality Theorem"

Similar presentations


Ads by Google