1.3b- Angles with parallel lines CCSS G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Transversal A line that intersects 2 or more coplanar lines at different points. transversal l m

Alternate Interior <s – Alternate Exterior <s - 2 3 4 l 5 6 7 8 m Interior <s - Exterior <s - Alternate Interior <s – Alternate Exterior <s - Consecutive Interior <s – Corresponding <s - <3, <4, <5, <6 (inside l & m) <1, <2, <7, <8 (outside l & m) <3 & <6, <4 & <5 (alternate –opposite sides of the transversal) <1 & <8, <2 & <7 <3 & <5, <4 & <6 (consecutive – same side of transversal) <1 & <5, <2 & <6, <3 & <7, <4 & <8 (same location)

Ex. n Name the following: Alt. Int- Alt ext- Corresponding- Consecutive int- Vertical- p m 2 &7 ; 5 &4 3 & 6 ; 1 & 8 1 2 3 5 1 & 5; 2 & 6 ; 4 & 8 ; 3 & 7 4 6 2 & 5 7 8 4 & 7 1 &4; 3 & 2; 5 & 8; 6 & 7

Identify any transversals

Corresponding s 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

Alt. Int. s 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

Alt. Ext. ’s 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

Consecutive Int. (same-side interior) 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

Consecutive Exterior. (same-side exterior) If 2  lines are cut by a transversal, then the pairs of consecutive exterior. s are supplementary. i.e. If l m, then 1 & 2 are supp. l m 1 2

 Transversal 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. t 1 2 l m

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

Ex.2. Solve for x and Find all the angle measures 8 4x-8 1 3 6x+ 12 4 6 9

Find m<1 Find m<1

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