3.3 Proofs with parallel lines

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3.3 Parallel Lines & Transversals

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Presentation transcript:

3.3 Proofs with parallel lines

What we will learn Use corresponding angles converse Prove lines parallel Use transitive property of parallel lines

Ex. 1 using theorems to prove parallel Find value of x that makes 𝑚∥𝑛 Corresponding angles congruent thm 3𝑥+5=65 −5 −5 3𝑥=60 3𝑥 3 = 60 3 𝑥=20 3x+5 m 65 n

Your Practice Find value of x that makes 𝑚∥𝑛 3𝑥−15+150=180 3𝑥+135=180 −135 −135 3𝑥=45 3𝑥 3 = 45 3 𝑥=15 150 3x-15

Ex. 2 proving lines parallel Statement Reason Given: ∠1 𝑎𝑛𝑑 ∠3 are supplementary Prove: 𝑚∥𝑛 1. ∠𝟏 𝒂𝒏𝒅 ∠𝟑 are supplementary 1. Given 2. ∠𝟏≅∠𝟐 2. Vertical angles 3. ∠𝟐 𝒂𝒏𝒅 ∠𝟑 are supplementary 3. substitution 1 m 2 4. 𝒎∥𝒏 4. Thm 3.8 3 n

Your practice Given: ∠1≅∠2, ∠3≅∠4 Prove: 𝐴𝐵 ∥ 𝐶𝐷 Statement Reason 1. ∠1≅∠2, ∠3≅∠4 1. Given 2. ∠2≅∠3 2. Vert. Angles 3. ∠1≅∠3 3. Trans. Prop 4. ∠1≅∠3 4. Trans. Prop 5. 𝐴𝐵 ∥ 𝐶𝐷 5. Thm 3.6 A D 1 E 2 3 4 B C

Ex. 3 is there enough information Given: 𝑟∥𝑠 𝑎𝑛𝑑 ∠1≅∠3 Can you prove 𝑝∥𝑞? Yes, because ∠1≅∠2 by corresponding angles. ∠2≅∠3 by substitution. Therefore 𝑝∥𝑞 by Thm 3.6. 3 p 2 1 q r s

Ex. 4 transitive property of parallel lines Find 𝑚∠8 115+𝑚∠8=180 −115 −115 𝑚∠8=65