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3.3 Parallel Lines & TransversalsGeometry
Standard/Objectives:Standard 3: Students will learn and apply geometric concepts. Objectives: Prove and use results about parallel lines and transversals. Use properties of parallel lines.
Post. 15 – Corresponding s Post.If 2 lines are cut by a transversal, then the pairs of corresponding s are . i.e. If l m, then 12. 1 2 l m
Thm 3.4 – Alt. Int. s Thm. If 2 lines are cut by a transversal, then the pairs of alternate interior s are . i.e. If l m, then 12. 1 2 l m
Proof of Alt. Int. s Thm. Statements l m 3 2 1 3 1 2Reasons Given Corresponding s post. Vert. s Thm is transitive 3 1 2 l m
Thm 3.5 – Consecutive Int. s thmIf 2 lines are cut by a transversal, then the pairs of consecutive int. s are supplementary. i.e. If l m, then 1 & 2 are supp. l m 1 2
Thm 3.6 – Alt. Ext. s Thm. If 2 lines are cut by a transversal, then the pairs of alternate exterior s are . i.e. If l m, then 12. l m 1 2
Thm Transversal Thm. If a transversal is to one of 2 lines, then it is to the other. i.e. If l m, & t l, then t m. ** 1 & 2 added for proof purposes. t 1 2 l m
Proof of transversal thmStatements l m, t l 12 m1=m2 1 is a rt. m1=90o 90o=m2 2 is a rt. t m Reasons Given Corresp. s post. Def of s Def of lines Def of rt. Substitution prop =
Ex: Find: m1= m2= m3= m4= m5= m6= x= 1 125o 2 3 5 x+15o
Ex: Find: m1=55° m2=125° m3=55° m4=125° m5=55° m6=125° x=40°125o 2 3 5 x+15o
Chapter 3.2 Notes: Use Parallel Lines and Transversals
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12. Conv. of corr. s post. 14. Both angles = 124°, Conv. of corr
CONFIDENTIAL 1 Geometry Proving Lines Parallel. CONFIDENTIAL 2 Warm Up Identify each of the following: 1) One pair of parallel segments 2) One pair of.
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Lesson 3-4 Proving lines parallel,. Postulates and Theorems Postulate 3-4 – If two lines in a plane are cut by a transversal so that corresponding angles.
Objective Use the angles formed by a transversal to prove two lines are parallel.
Holt McDougal Geometry 3-3 Proving Lines Parallel Bellringer State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°,
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Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If m A + m B = 90°, then A and B are complementary. 3. If AB.
Proving Lines Parallel 3.4. Use the angles formed by a transversal to prove two lines are parallel. Objective.
3.2 Use Parallel Lines and Transversals. Objectives Use the properties of parallel lines to determine congruent angles Use algebra to find angle measures.
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