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Understanding Angle Relationships and Theorems in Geometry

This guide explores key theorems related to angles, including definitions and proofs of angle relationships. Theorem 2-2 states that angles forming a linear pair are supplementary. Theorems 2-3 highlights the properties of angle congruence: reflexive, symmetric, and transitive. Theorems 2-4 and 2-5 address the congruence of supplementary and complementary angles. Additional theorems reveal that all right angles are congruent, vertical angles are congruent, and that perpendicular lines intersect to form four right angles.

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Understanding Angle Relationships and Theorems in Geometry

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  1. Unit 2.6 Verifying Angle Relationships

  2. Theorem 2-2 • If two angles form a linear pair, then they are supplementary.

  3. Theorem 2-3 • Congruence of angles is reflexive, symmetric and transitive. REFLEXIVE: <ABC = <ABC SYMMETRIC: If <ABC = <CDE, then <CDE = <ABC TRANSITIVE: If <ABC = <CDE and <CDE = <FGH, then <ABC = <FGH

  4. Theorem 2-4 • Angles supplementary to the same angle or to congruent angles are congruent.

  5. Theorem 2-5 • Angles complementary to the same angle or to congruent angles are congruent.

  6. Theorem 2-6 • All right angles are congruent.

  7. Theorem 2-7 • Vertical Angles are congruent.

  8. Theorem 2-8 • Perpendicular lines intersect to form four right angles.

  9. NOW LETS LOOK AT SOME PROoFS

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