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2.6 Proving Angle Relationships

2.6 Proving Angle Relationships. Objective: Students will write proofs involving supplementary & complementary angles, congruent and right angles. 2.6 Postulates and Theorems. Angle Addition Postulate : If R is in the interior of angle PQS, then m<PQR + m<RQS = m<PQS.

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2.6 Proving Angle Relationships

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  1. 2.6 Proving Angle Relationships Objective: Students will write proofs involving supplementary & complementary angles, congruent and right angles.

  2. 2.6 Postulates and Theorems • Angle Addition Postulate: If R is in the interior of angle PQS, then m<PQR + m<RQS = m<PQS. • Supplement Theorem: If 2 angles form a linear pair, then they are supplementary. • Complement Theorem: If the noncommon sides of 2 adjacent angles form a right angle, then the angles are complementary. P R Q S

  3. 2.6 Postulates and Theorems • Congruence of angles is reflexive, symmetric, and transitive. • Angles supplementary to the same angle or congruent angles are congruent. • Angles complementary to the same angle or congruent angles are congruent. • Vertical Angles Theorem: If 2 angles are vertical angles, then they are congruent.

  4. 2.6 Postulates and Theorems • Perpendicular line form 4 right angles. • All right angles are congruent. • Perpendicular lines form adjacent congruent angles. • If 2 angles are congruent and supplementary, then they are right angles. • If 2 congruent angles form a linear pair, then they are right angles.

  5. Examples Find the measure of each numbered angle.

  6. Examples

  7. Example 1Answer

  8. Example 2

  9. Example 2Answer

  10. Example 3

  11. Example 3 Answer

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