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Corresponding Angles Postulate

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.

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Corresponding Angles Postulate

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

  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

  3. 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°

  4. 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

  5. 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

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

  7. ∠ 4∠ 5 GIVEN : gh PROVE : EXAMPLE 2 Prove the Alternate Interior Angles Converse SOLUTION

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

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

  10. Given: rsand 1 is congruent to 3. Prove: pq. REASONS STATEMENTS 1. pq rs 3. Given 4. 5. 4. 1∠ 2 2∠ 3 1∠ 3 Alternate Interior Angles Substitution 2. 3. Given 1. 5 2. Corresponding Angles EXAMPLE 3 EXAMPLE 4 Write a paragraph proof

  11. EXAMPLE 4 Given: m || n, n || kProve: m || k 1 m 2 n 3 k

  12. REASONS STATEMENTS EXAMPLE 3 EXAMPLE 3

  13. 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 • Def of rt.  • Def of  lines

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