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Chapters 2 – 4 Proofs practice
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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 1. 2. 3. 4. 5. 6. 1. Given 2. Angle Add. Postulate 3. Substitution Property 4. Subtraction Prop = 5. Transitive Property 6. Definition of bisect
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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 1. 2. 3. 4. 5. 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
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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
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Chapter 3 Proofs Practice Commonly used properties, definitions, and postulates, and theorems StatementsReasons 1. 2. 3. 4. 5. 6. 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
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Alternative interior angles theorem Alternative exterior angles theorem Same-side interior angles theorem Corresponding angle postulate StatementsReasons 1. 2. 3. 4. 5. 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
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StatementsReasons 1. 2. 3. 4. 5. 6. 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
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SSS SAS ASA AAS HL StatementsReasons 1. 2. 3. 4. 5. 6. Triangle sum theorem Exterior angles theorem Isosceles triangle theorem Isosceles triangle converse Definition of congruent triangles (CPCTC) 1 2 1. Given 2. Given 3. Def. of 4. Isos. Triangle converse 5. HL 6. CPCTC
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SSS SAS ASA AAS HL StatementsReasons 1. 2. 3. 4. 5. 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
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