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31 Corresponding Angles Postulate 

Definition
If a transversal intersects 2 parallel lines, then corresponding angles are congruent



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Theorem 31 Alternate Interior Angles 

Definition
If a transversal intersects 2 parallel lines, then alternate interior angles are congruent 


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Theorem 32 Sameside Interior Angles 

Definition
If a transversal intersects 2 parallel lines, then same side interior angles are supplementary m<1 + m<2 = 180 


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is a line that intersects 2 lines a differnt planes (coplaner) at 2 points. 


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statements that are assumed to be true without proof. Postulates serve two purposes  to explain undefined terms, and to serve as a starting point for proving other statements. 


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are statements that can be deduced and proved from definitions, postulates, and previously proved theorums. 


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any pair of angles in similar locations with respect to a transversal 


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the angle formed by the equilateral (equal in length) sides of an isoscoles triangle 


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a triangle with two sides of equal length 


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33 Alternate Exterior Theorem 

Definition
If a transversal intersects 2 parallel lines, then alternate exterior angles are congruent 


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34 Same Side Exterior Angles 

Definition
If a transversal intersects 2 parallel lines, the sameside exterior angles are supplementary m<2 + m<3 = 180 


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Postulate 32 Converse of Corresponding Angles Postulate 

Definition
if two lines and a transversal line form corresponding angles which are congruent, then the two lines are parralle 


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Theoreom 35 Converse of Alternate Interior Angles Theorem 

Definition
if two lines and a transversal line form alternate interior angles which are congruent, then the two lines are parralle 


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Theoreom 36 Converse of Same Side Interior Angles Theorem 

Definition
if two lines and a transversal line form sameside interior angles which are congruent, then the two lines are parralle 


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Definition
Arrrows show the logical connections between the statements. The reasons are written below the statements 


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Theoreom 37 Converse of Alternate Exterior Angles Theorem 

Definition
if two lines and a transversal line form alternate exterior angles which are congruent, then the two lines are parralle 


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Theoreom 38 Converse of Same Side Exterior Angles Theorem 

Definition
if two lines and a transversal line form sameside exterior angles which are congruent, then the two lines are parralle 


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Definition
If 2 lines are parrallel to the same line, then they are parallel to each other 


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In a plane, if two lines are perpendicular to the same line, then they are parrallel 


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Definition
If a line is perpendicular to one of two parrallel lines, then it is also perpendicular to the other line 


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Theorem 312 Triangle AngleSum Theorem 

Definition
The sum of the measures of the angles of a triangle is 180 


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Theorem 313 Triangle Exterior Angle Theorem 

Definition
The measure of each exterior angle of a triangle equals the sume of the measures of its two remote interior angles 


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is a closed plan figure with at least 3 sides that are segements 


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has no diagonal with points outside the polygon 


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Has at least one diagonal with points outside the polygan 


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Theorem 314 Polygon AngelSum Theorem 

Definition
The sum of the measures of the angles of an ngon is (n2)180. 


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Theorem 315 Polygon Exterior AngleSum Theorem 

Definition
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. 


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both equilateral and equianglar 

