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Angles and Parallel Lines. Congruent Complements Theorem. If ∠4 and ∠5 are complementary and ∠5 and ∠6 are complementary Then ∠4 ∠6. Congruent Supplements Theorem. If ∠1 and ∠2 are supplementary and ∠2 and ∠3 are supplementary Then ∠1 ∠3. Transversal.

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Presentation Transcript
congruent complements theorem
Congruent Complements Theorem

If ∠4 and ∠5 are complementary

and ∠5 and ∠6 are complementary

Then

∠4 ∠6

congruent supplements theorem
Congruent Supplements Theorem
  • If ∠1 and ∠2 are supplementary

and ∠2 and ∠3 are supplementary

Then

∠1 ∠3

transversal
Transversal
  • Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
  • When a transversal t intersects line n and m, eight angles of the following types are formed:

Exterior angles

Interior angles

Consecutive angles

Alternate angles

t

m

n

corresponding angles
Corresponding Angles

Corresponding Angles: Two angles that occupy corresponding positions.

Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the Corresponding angles are congruent.

 2  6, 1  5,3  7,4  8

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same side or consecutive angles
Same Side or Consecutive Angles

Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.

Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Interior Angles are supplementary.

m3 +m5 = 180º, m4 +m6 = 180º

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alternate angles
Alternate Angles
  • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair).
  • Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Interior Angles are congruent.

3  6,4  5

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alternate angles1
Alternate Angles
  • Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.
  • Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Exterior Angles are congruent.

2  7,1  8

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