Angles Postulates & Theorems

Angles Postulates & Theorems 1-4 1-5

Warm Up n

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AC of B is the Midpoint . Find x, AB, and AC if AB = x2 + 3 and BC = 5x - 1 E is between D and F. Find x, EF, and DF if DE = 8, EF = 7x, and DF = x2

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1.4 Angles An angle is formed by two rays that have the same endpoint  The two rays are called the sides of the angle, and their common endpoint is the vertex of the angle  Angles can be named using three letters or in some cases just one letter (the vertex) 

Special Angles Acute angle – measure between 0 and 90 (it’s a cute angle!)  Right angle – measure 90  Obtuse angle – measure between 90 and 180  Straight angle - measure 180 

How angles relate to each other Adjacent angles are two angles in a plane that have a common vertex and a common side, but no common interior points  Bisector of an angle is the ray that divides the angle into two congruent adjacent angles  Congruent Angles have equal measure 

Angle Addition Postulate 

If point B lies in the∠AOC interior =  ∠ ofm∠ +  ∠ , then

∠AOC

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suur AC

If is a straight B +is  ∠any  point =  not on anglem∠ and , then

Ex. 1 What do you know is TRUE? What do you know is NOT TRUE?

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Ex. 2

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1-5 Postulates & Theorems 

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Postulates: We accept as fact without proof Assumptions are postulates

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Theorems: Statements that require proof You cannot assume that theorems are true unless they have been proven

Postulates - do not copy!! A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points all in one plane.  Through any two points there is exactly one line. 

More postulates - do not copy!! Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.  If two points are in a plane, then the line that contains the points is in that plane.  If two planes intersect, then 

Theorems - do not copy!! If two lines intersect, then they intersect in exactly one point.  Through a line and a point not in the line there is exactly one plane.  If two lines intersect, then exactly one plane contains the lines. 