Lesson 2 8 Proving Angle Relationships Write proofs

Postulate 2. 11 Angle Addition Postulate o If R is in the interior of

Theorems 2. 3 Supplement Theorem o If two angles form a linear pair, then

Theorem 2. 4 Complement Theorem o If the noncommon sides of two adjacent angles

Theorem 2. 5 o o Congruence of angles is reflexive, symmetric, and transitive. Reflexive

Theorem 2. 6 n n Angles supplementary to the same angle are congruent. Angles

Theorem 2. 7 o o Angles complementary to the same angle are congruent. Angles

Theorem 2. 8 Vertical Angle Theorem o If two angles are vertical angles, then

Theorems o o o 2. 9: Perpendicular lines intersect to form four right angles.

Theorems o o 2. 12: If two angles are congruent and supplementary, then each

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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 o If R is in the interior of <PQS, then m<PQS + m<RQS = m< PQS

Theorems 2. 3 Supplement Theorem o If two angles form a linear pair, then they are supplementary angles.

Theorem 2. 4 Complement Theorem o If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

Theorem 2. 5 o o 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, o then <1 =<3.

Theorem 2. 6 n n Angles supplementary to the same angle are congruent. Angles supplementary to congruent angles are congruent.

Theorem 2. 7 o o Angles complementary to the same angle are congruent. Angles complementary to congruent angles are congruent.

Theorem 2. 8 Vertical Angle Theorem o If two angles are vertical angles, then they are congruent.

Theorems o o o 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.

Theorems o o 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.