Corresponding Angles Postulate If two parallel lines are

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Corresponding Angles Postulate • If two parallel lines are cut by a transversal, then

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

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

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

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

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

EXAMPLE 1 Review State the postulate or theorem that justifies the statement. b a

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

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

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

EXAMPLE 2 Prove the Alternate Interior Angles Converse REASONS STATEMENTS 1. 4∠ 1∠ 2.

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

EXAMPLE 3 Prove the Alternate Interior Angles Converse Theorem p q GIVEN : PROVE

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

EXAMPLE 3 4 Given: r Write a paragraph proof and s Prove: p 1

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

EXAMPLE 4 Given: m || n, n || k Prove: m || k Statements

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

STATEMENTS EXAMPLE 3 REASONS

STATEMENTS EXAMPLE 3 REASONS

Given: l m, & t l, Proof: t m. Statements 1. l m, t

Given: l m, & t l, Proof: t m. Statements 1. l m, t l 2. 3. 4. 5. 6. 7. 8. 1 2 m 1=m 2 1 is a rt. m 1=90 o 90 o=m 2 2 is a rt. t m t 1. 2. 3. 4. 5. 6. 7. 8. 1 l 2 m Reasons Given Corresponding angles Def of lines Def of rt. Substitution Def of rt. Def of lines

PROPERTIES OF PARALLEL LINES POSTULATE 15 Corresponding AnglesPROPERTIES OF PARALLEL LINES POSTULATE 15 Corresponding Angles
PROPERTIES OF PARALLEL LINES POSTULATE 15 Corresponding AnglesPROPERTIES OF PARALLEL LINES POSTULATE 15 Corresponding Angles
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3 3 Parallel Lines Transversals Postulate 16 Corresponding3 3 Parallel Lines Transversals Postulate 16 Corresponding
Lines and Angles Geometry PARALLEL LINES Two linesLines and Angles Geometry PARALLEL LINES Two lines
Parallel Lines and Angles Vertical Angles Vertical AnglesParallel Lines and Angles Vertical Angles Vertical Angles
Parallel and Perpendicular Lines Parallel Lines Two linesParallel and Perpendicular Lines Parallel Lines Two lines
GEOMETRY Angles and Parallel Lines Intersecting Lines LinesGEOMETRY Angles and Parallel Lines Intersecting Lines Lines
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