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Published byAlfred Ingman Modified over 2 years ago

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3.3 Parallel Lines & Transversals Geometry

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Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: 1.Prove and use results about parallel lines and transversals. 2.Use properties of parallel lines.

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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 1 2. l m 1 2

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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 1 2. lmlm 1 2

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Proof of Alt. Int. s Thm. Statements 1.l m 2. 3 2 3. 1 3 4. 1 2 Reasons 1.Given 2.Corresponding s post. 3.Vert. s Thm 4. is transitive lmlm 1 2 3

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Thm 3.5 – Consecutive Int. s thm If 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. lmlm 1 2

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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 1 2. l m 1 2

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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. 1 2 Thm 3.7 - Transversal Thm. lmlm t

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Proof of transversal thm Statements 1.l m, t l 2. 1 2 3.m 1=m 2 4. 1 is a rt. 5.m 1=90 o 6.90 o =m 2 7. 2 is a rt. 8.t m Reasons 1.Given 2.Corresp. s post. 3.Def of s 4.Def of lines 5.Def of rt. 6.Substitution prop = 7.Def of rt. 8.Def of lines

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Ex: Find: m 1= m 2= m 3= m 4= m 5= m 6= x= 125 o 2 1 3 4 6 5 x+15 o

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Ex: Find: m 1=55 ° m 2=125 ° m 3=55 ° m 4=125 ° m 5=55 ° m 6=125 ° x=40 ° 125 o 2 1 3 4 6 5 x+15 o

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