3.3 Parallel Lines & Transversals Geometry

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 12. 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 12. 1 2 l m

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

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

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

Thm 3.7 -  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 thm Statements l m, t  l 12 m1=m2 1 is a rt.  m1=90o 90o=m2 2 is a rt.  t m Reasons Given Corresp. s post. Def of  s Def of  lines Def of rt.  Substitution prop =

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

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