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Chapter 6 lesson 2

Chapter 6 lesson 2. Properties of Parallelograms. Warm-up. ASA. HGE. GHE. HEG. GH. HE. EG. They are parallel. Theorem 6.1. Opposite sides of a parallelogram are congruent. Consecutive Angles. Angles of a polygon that share a side are consecutive angles.

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Chapter 6 lesson 2

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  1. Chapter 6 lesson 2 Properties of Parallelograms

  2. Warm-up ASA HGE GHE HEG GH HE EG They are parallel.

  3. Theorem 6.1 • Opposite sides of a parallelogram are congruent.

  4. Consecutive Angles • Angles of a polygon that share a side are consecutive angles. • Because opposite sides of a parallelogram are parallel, consecutive angles are same-side interior angles • They are therefore SUPPLEMENTARY. • ∠a and ∠d are consecutive angles m∠a + m∠d = 180

  5. Theorem 6-2 • Opposite angles of a parallelogram are congruent Opposite angles are supplements of the same angle. Therefore, they are congruent.

  6. Theorem 6-3 • The diagonals of a parallelogram bisect each other

  7. Proof of Theorem 6.3 • Given: Parallelogram ABCD Prove: AC and BD bisect each other at point O • If ABCD is a parallelogram, then AB and DC are parallel. • ∠1≅ ∠4 and ∠2≅ ∠3 because alternate Interior angles are congruent. • AB ≅ DC because opposite sides of a parallelogram are congruent. • ∆ADO ≅ ∆BCO by ASA • AE≅CE and BE≅DE by CPCTC 4 2 1 3

  8. Theorem 6.4 • If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  9. Example 1: Using Consecutive Angles What is the measure of ∠P? Consecutive angles are supplementary 64 + P = 180 P = 180 – 64 P = 116

  10. Your Turn! Consecutive angles are supplementary 86 + P = 180 P = 180 –86 P = 94

  11. Example 2: Proofs

  12. Proof #2

  13. Example 3: Algebra

  14. Your Turn! Algebra

  15. Example 4: Parallel Lines and Transversals

  16. Lesson Quiz

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