Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 1 ≅ 2

Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4 3 ≅ 4

Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 5 6 5 + 6 = 180°

Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 7 8 7 ≅ 8

Perpendicular Transversal If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other. j h k j  k

State the postulate or theorem that justifies the statement. EXAMPLE 1 Review State the postulate or theorem that justifies the statement. b a > c d f e > g h

EXAMPLE 2 Prove the Alternate Interior Angles Converse SOLUTION GIVEN : ∠ 4 ∠ 5 PROVE : g h

Prove the Alternate Interior Angles Converse EXAMPLE 2 Prove the Alternate Interior Angles Converse STATEMENTS REASONS 1. 4 ∠ 5 1. Given 2. Vertical Angles Congruence Theorem 2. 1 ∠ 4 3. Transitive Property of Congruence 3. 1 ∠ 5 4. Corresponding Angles Converse g h 4.

Prove the Alternate Interior Angles Theorem EXAMPLE 3 EXAMPLE 3 Prove the Alternate Interior Angles Theorem Prove the Alternate Interior Angles Converse GIVEN : p q PROVE : ∠ 1 ∠ 2 STATEMENTS REASONS 1. Given 1. p q 2. Vertical Angles 2. 3 ∠ 2 3. Corresponding Angles 3. 1 ∠ 3 4. 1 ∠ 2 4. Transitive Property

Write a paragraph proof EXAMPLE 3 EXAMPLE 4 Write a paragraph proof Given: r s and 1 is congruent to 3. Prove: p q. STATEMENTS REASONS r s 1. 1. Given 2. Corresponding Angles 2. 1 ∠ 2 3. Given 3. 1 ∠ 3 4. Substitution 4. 2 ∠ 3 p q 5 5. Alternate Interior Angles

Given: m || n, n || k Prove: m || k EXAMPLE 4 Given: m || n, n || k Prove: m || k Statements Reasons 1. m || n 1. Given 2. 2. Corresponding 3. n || k 3. Given 4. 4. Corresponding 5. 5. Transitive 6. m || k 6.Corresponding 1 m 2 n 3 k

REASONS STATEMENTS EXAMPLE 3 EXAMPLE 3

Statements Reasons l m, t  l Given 12 Corresponding angles Given: l m, & t  l, Proof: t m. t 1 2 l m Statements l m, t  l 12 m1=m2 1 is a rt.  m1=90o 90o=m2 2 is a rt.  t m Reasons Given Corresponding angles Def of  s Def of  lines Def of rt.  Substitution