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Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles
Properties of Angle Congruence Theorem 2.2 Reflexive: Transitive : Symmetric:
Two-Column Proof Using Transitive Property Given:Prove: Statements Reasons 8 4 1 7 3 2 6 5
Theorem 2.3 Right Angle Congruence Theorem All right angles are congruent.
Theorem 2.4 Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. 1 3 2
Theorem 2.5 Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles), then they are congruent. 4 56
Theorem 2.6 Vertical Angles Theorem Vertical angles are congruent. 1 4 3 2
Postulate 12 Linear Pair Postulate If two angles form a linear pair, then they are supplementary. 12
Given: Prove: Statements Reasons 1 3 2
Definitions you should know! Perpendicular lines Right angle Supplementary angles Complementary angles Segment bisector Angle bisector Linear pair Vertical angles Also, review Segment Addition Postulate & Angle Addition Postulate
Sec 2-6 Concept: Proving statements about segments and angles Objective: Given a statement, prove it as measured by a s.g.
Lesson 2 – 8 Proving Angle Relationships
Bell Work 1) Solve for each variable 2) Solve for each variable 3 and 4) Transitive Property of equality Definition of Congruence Given Definition of Congruence.
2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.
Proving Angle Relationships
DEFINITIONS, POSTULATES, AND PROPERTIES Review HEY REMEMBER ME!!!!!!
Use right angle congruence
2.6 Proving Statements about Angles Mrs. Spitz GeometryFall 2004.
2.6 Proving Statements about Angles
Warm Up Given: ∠ 1 ≅ ∠ 2 m ∠ 2 = 60° m ∠ 3 = 60° Prove: ∠ 1 ≅ ∠
2.6 Proving Statements about Angles Geometry. Standards/Objectives Students will learn and apply geometric concepts. Objectives: Use angle congruence.
Chapter 2.7 Notes: Prove Angle Pair Relationships
Chapter 2.7 Notes: Prove Angle Pair Relationships Goal: You will use properties of special pairs of angles.
2.6 Proving Statements about Angles. Properties of Angle Congruence ReflexiveFor any angle, A
Reasoning & Proof Chapter 2.
Prove Theorems Advanced Geometry Deductive Reasoning Lesson 4.
Warm-Up Exercises Lesson 2.7, For use with pages Give a reason for each statement. 1. If m 1 = 90º and m 2 = 90º, then m 1 = m If AB BC,
P. 114: 23 – 28. Given Transitive prop. congruence Definition of congruence Given Transitive prop. Equality/Substitution.
Verifying Angle Relations. Write the reason for each statement. 1) If AB is congruent to CD, then AB = CD Definition of congruent segments 2) If GH =
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