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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: Prove and use results about parallel lines and transversals. 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 12. 1 2 l m

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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 12. 1 2 l m

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**Proof of Alt. Int. s Thm. Statements l m 3 2 1 3 1 2**

Reasons Given Corresponding s post. Vert. s Thm is transitive 3 1 2 l m

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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. l m 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 12. l m 1 2

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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

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**Proof of transversal thm**

Statements 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 =

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Ex: Find: m1= m2= m3= m4= m5= m6= x= 1 125o 2 3 5 x+15o

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**Ex: Find: m1=55° m2=125° m3=55° m4=125° m5=55° m6=125° x=40°**

125o 2 3 5 x+15o

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