Chapter 6 lesson 2
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Transcript of Chapter 6 lesson 2
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CHAPTER 6 LESSON 2Properties of Parallelograms
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Warm-up
ASAHGE GHEHEG GH
HE EG
They are parallel.
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Theorem 6.1 Opposite sides of a parallelogram are
congruent.
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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
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Theorem 6-2 Opposite angles of a parallelogram are
congruent Opposite angles are supplementsof the same angle.
Therefore, they are congruent.
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Theorem 6-3 The diagonals of a parallelogram bisect
each other
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Proof of Theorem 6.3 Given: Parallelogram ABCD Prove: AC and BD bisect each other at
point O If ABCD is a parallelogram, thenAB and DC are parallel. ∠1 4 and 2 3 because ≅ ∠ ∠ ≅ ∠alternate Interior angles are congruent. AB ≅ DC because opposite sidesof a parallelogram are congruent. ∆ADO ≅ ∆BCO by ASA AE≅CE and BE≅DE by CPCTC
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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.
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Example 1: Using Consecutive Angles
What is the measure of ∠P?
Consecutive angles are supplementary
64 + P = 180 P = 180 – 64 P = 116
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Your Turn!
Consecutive angles are supplementary
86 + P = 180 P = 180 –86P = 94
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Example 2: Proofs
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Proof #2
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Example 3: Algebra
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Your Turn! Algebra
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Example 4: Parallel Lines and Transversals
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Lesson Quiz
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