Chapters 2 – 4 Proofs practice

Chapter 2 Proofs Practice Commonly used properties, definitions, and postulates  Transitive property  Substitution property  Definition of congruent  Segment addition postulate  Angle addition postulate  Right angles theorem  Definition of supplementary  Definition of complementary  Definition of midpoint  Definition of bisect  Linear pair postulate  Vertical angles theorem  Subtraction property Provide the missing reasons in the following proofs: StatementsReasons Given 2. Angle Add. Postulate 3. Substitution Property 4. Subtraction Prop = 5. Transitive Property 6. Definition of bisect

 Reflexive property  Transitive property  Substitution property  Definition of congruent  Segment addition postulate  Angle addition postulate  Right angles theorem  Definition of supplementary  Definition of complementary  Definition of midpoint  Definition of bisect  Linear pair postulate  Vertical angles theorem  Subtraction property StatementsReasons Given: 1 and 2 are supplementary, and 1  3 Prove: 3 and 2 are supplementary. 1. Given 2. Definition of Supplementary 3. Definition of . 4. Substitution Property 5. Definition of supplementary

 Reflexive property  Transitive property  Substitution property  Definition of congruent  Segment addition postulate  Angle addition postulate  Right angles theorem  Definition of supplementary  Definition of complementary  Definition of midpoint  Definition of bisect  Linear pair postulate  Vertical angles theorem  Subtraction property m  3 + m  4 = 90 °  3 and  4 are comp. Prove:  3 and  4 are complementary Given:  1 and  2 are complementary Given Definition of Complementary Vertical Angles Theorem Definition of Congruent Substitution Property Def. of complementary

Chapter 3 Proofs Practice Commonly used properties, definitions, and postulates, and theorems StatementsReasons  Alternative interior angles theorem  Alternative exterior angles theorem  Same-side interior angles theorem  Corresponding angle postulate  Alternative interior angles converse  Alternative exterior angles converse  Same-side interior angles converse  Corresponding angle converse  Perpendicular transversal theorem Linear Pair Theorem Alt. Ext. Angles Th. Same-side int  s Th. Vertical  s Th. Alt. Int.  s Th Corr.  s Postulate

 Alternative interior angles theorem  Alternative exterior angles theorem  Same-side interior angles theorem  Corresponding angle postulate StatementsReasons  Alternative interior angles converse  Alternative exterior angles converse  Same-side interior angles converse  Corresponding angle converse  Perpendicular transversal theorem 1. Given 2. Vertical Angles Th 3. Vertical Angles Th 4. Substitution Property 5. Same-side int angles converse

StatementsReasons  SSS  SAS  ASA  AAS  HL  Triangle sum theorem  Exterior angles theorem  Isosceles triangle theorem  Isosceles triangle converse  Definition of congruent triangles (CPCTC) Chapter 4 Proofs Practice Commonly used properties, definitions, and postulates, and theorems ASA 6. ASA 1. Given 2. Given 3. All rt  s are congruent 4. Def. of Midpoint 5. Vertical Angles theorem

 SSS  SAS  ASA  AAS  HL StatementsReasons  Triangle sum theorem  Exterior angles theorem  Isosceles triangle theorem  Isosceles triangle converse  Definition of congruent triangles (CPCTC) Given 2. Given 3. Def. of  4. Isos. Triangle converse 5. HL 6. CPCTC

 SSS  SAS  ASA  AAS  HL StatementsReasons  Triangle sum theorem  Exterior angles theorem  Isosceles triangle theorem  Isosceles triangle converse  Definition of congruent triangles (CPCTC) Justify each statement using the figure. Linear Pair Theorem Ext. angles Theorem Triangle Sum Theorem Exterior angles theorem Isosceles Triangle Theorem