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3.3 Parallel Lines & Transversals Geometry. Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: 1.Prove and.

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Presentation on theme: "3.3 Parallel Lines & Transversals Geometry. Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: 1.Prove and."— Presentation transcript:

1 3.3 Parallel Lines & Transversals Geometry

2 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.

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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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