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Section 2.6: Proving Statements about Angles

Section 2.6: Proving Statements about Angles. Goals . Use Angle Congruence Properties Prove Properties about Special Pairs of Angles. Theorem 2.2: Properties of Angle Congruence . Angle congruence is reflexive, symmetric and transitive. Examples Reflexive

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Section 2.6: Proving Statements about Angles

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  1. Section 2.6: Proving Statements about Angles

  2. Goals • Use Angle Congruence Properties • Prove Properties about Special Pairs of Angles

  3. Theorem 2.2: Properties of Angle Congruence • Angle congruence is reflexive, symmetric and transitive. • Examples • Reflexive • For any angle A, then angle A  angle A • Symmetric • If A  B, then B A • Transitive • If A  B and B  C, then A C

  4. Theorem 2.3: Right Angle Congruence Theorem • All right angles are congruent Theorem 2.4: Congruent Supplement Theorem • If m1 + m2 = 180° and m2 + m3 = 180°, then 1 3

  5. Theorem 2.5: Congruent Complement Theorem • If m1 + m2 = 90° and m2 + m3 = 90°, then 1 3 Postulate 12: Linear Pair Postulate • If two angles form a linear pair, then they are supplementary

  6. Theorem 2.6: Vertical Angles Theorem • Vertical angles are congruent

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