Study Guide-2 column Proof Reasons
Properties of Equality (POE): Used for Algebra, Numbers, and Measures
1) Reflexive POE
2) Symmetric POE
3) Transitive POE
4) Addition POE
5) Subtraction POE
6) Multiplication POE
7) Division POE
8) Substitution POE
9) Distributive POE
10) Simplification POE
Properties of Congruence (POC): Used for Parts of Shapes
1) Reflexive POC
2) Symmetric POC
3) Transitive POC
Definitions, Postulates, and Theorems pertaining to Angles:
1) Definition of Vertical Angles
2) Definition of Complementary Angles
3) Definition of Supplementary Angles
4) Definition of Linear Pair of Angles
5) Definition of Congruent Angles
6) Definition of Angle Bisector
7) Angle Addition Postulate
8) Linear Pair of Angles Postulate
9) Vertical Angle Theorem
10) Congruent Complement Theorem
11) Congruent Supplement Theorem
12) Right Angle Congruence Theorem
13) Perpendicular Transversal Theorem
Definitions, Postulates, and Theorems pertaining to Segments:
1) Definition of Midpoint
2) Definition of Segment Bisector
3) Definition of Perpendicular Lines
4) Definition of Perpendicular Bisector
5) Definition of an Isosceles Triangle
6) Definition of an Equilateral Triangle
7) Segment Addition Postulate
Ways to Prove Angles are Congruent or Supplementary Given Parallel Lines:
1) Corresponding Angles Theorem (congruent)
2) Alternate Interior Angles Theorem (congruent)
3) Alternate Exterior Angles Theorem (congruent)
4) Vertical Angles Theorem (congruent)
5) Same Side Interior Angles Theorem (supplementary)
6) Linear Pair of Angles Theorem (supplementary)
Ways to Prove Parallel Lines Given Congruent or Supplementary Angles:
1) Converse of Corresponding Angles Theorem (congruent)
2) Converse of Alternate Interior Angles Theorem (congruent)
3) Converse of Alternate Exterior Angles Theorem (congruent)
4) Converse of Same Side Interior Angles Theorem (supplementary)
5) Converse of Linear Pair of Angles Theorem (supplementary)
6) Transitive Property of Parallel Lines
7) Property of Perpendicular Lines
Other Important Information:
1) InteriorInside Parallel Lines
2) Exterior Outside Parallel Lines
3) AlternateOpposite Sides of the Transversal
4) Same Side Same Side of the Transversal
5) Corresponding Same/Similar Position on Parallel Lines and Transversal
6) Transversal: Line that cuts a pair of parallel lines resulting in the formation of
congruent and supplementary angle relationships