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Lesson 2-8 Proving Angle Relationships

Lesson 2-8 Proving Angle Relationships. •Write proofs involving supplementary and complementary angles. •Write proofs involving congruent and right angles. Postulate 2.11 Angle Addition Postulate. If R is in the interior of <PQS, then m<PQS + m<RQS = m< PQS.

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Lesson 2-8 Proving Angle Relationships

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  1. Lesson 2-8Proving Angle Relationships •Write proofs involving supplementary and complementary angles. •Write proofs involving congruent and right angles.

  2. Postulate 2.11Angle Addition Postulate • If R is in the interior of <PQS, then m<PQS + m<RQS = m< PQS

  3. Theorems 2.3Supplement Theorem • If two angles form a linear pair, then they are supplementary angles.

  4. Theorem 2.4Complement Theorem • If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

  5. Theorem 2.5 • Congruence of angles is reflexive, symmetric, and transitive. • Reflexive Property: <1 = < 2 • Symmetric Property: If <1 = < 2, then <2 = <1. • Transitive Property: If <1 = <2 and <2 =<3, • then <1 =<3.

  6. Theorem 2.6 • Angles supplementary to the same angle are congruent. • Angles supplementary to congruent angles are congruent.

  7. Theorem 2.7 • Angles complementary to the same angle are congruent. • Angles complementary to congruent angles are congruent.

  8. Theorem 2.8Vertical Angle Theorem • If two angles are vertical angles, then they are congruent.

  9. Theorems • 2.9: Perpendicular lines intersect to form four right angles. • 2.10: All right angles are congruent. • 2.11: Perpendicular lines form congruent adjacent angles.

  10. Theorems • 2.12: If two angles are congruent and supplementary, then each angle is a right angle. • 2.13: If two congruent angles form a linear pair, then they are right angles.

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