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7-3: Exterior Angle Inequality Theorem
Proof Geometry
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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.
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Exterior Angle formal Defintion
If C is between A and D, then BCD is an exterior angle of ABC
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Every triangle has 6 exterior angles.
2 1 3 X 4 6 5 X X = not exterior angles
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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
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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
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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.
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Corollary Exterior Angle Inequality
If a triangle has one right angle, then its other angles are acute.
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Corollary Exterior Angle Inequality
If a triangle has one right angle, then its other angles are acute. You try!
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Given: The figure Prove: ∠A<∠𝐷𝐸𝐹
You Try! DEF > B Ext. Ineq. Theorem B > A Ext. Ineq. Theorem DEF > A Transitive prop. of ineq.
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Homework pg : #1-10
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