Parallel Lines & Transversals
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1 Parallel Lines & Transversals
2 Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A C Interior B D A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol is used to indicate parallel lines. AB CD
3 Parallel Lines and Transversals A slash through the parallel symbol indicates the lines are not parallel. A B D AB CD C
4 Transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. Interior Parallel lines Non-Parallel lines Interior transversal transversal
5 Parallel Lines and Transversals Transversal - A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. j k m t Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.
6 INTERIOR The space INSIDE the 2 lines interior EXTERIOR -The space OUTSIDE the 2 lines exterior exterior
7 Special Angle Relationships Interior Interior Angles <3 & <6 are Alternate Interior angles <4 & <5 are Alternate Interior angles <3 & <5 are Same Side Interior angles <4 & <6 are Same Side Interior angles Angles <1 & <8 are Alternate angles <2 & <7 are Alternate angles <1 & <7 are Same Side angles <2 & <8 are Same Side angles
8 Special Angle Relationships WHEN THE LINES ARE PARALLEL 1 3 Interior If the lines are not parallel, these angle relationships DO NOT EXIST. Alternate Interior Angles are CONGRUENT Alternate Angles are CONGRUENT Same Side Interior Angles are SUPPLEMENTARY Same Side Angles are SUPPLEMENTARY
9 Corresponding Angles & Consecutive Angles Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5, 3 7, Interior
10 Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. L Line L G GPB = PQE A P B Line M GPA = PQD D Q F E Line N BPQ = EQF APQ = DQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.
11 Same Side Interior/ Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. m 3 +m 5 = 180º, m 4 +m 6 = 180º Same Side Angles: Two angles that lie outside parallel lines on the same sides of the transversal. 1 2 m 1 +m 7 = 180º, m 2 +m 8 = 180º Interior
12 Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. m 3 +m 5 = 180º, m 4 +m 6 = 180º Consecutive Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m 1 +m 7 = 180º, m 2 +m 8 = 180º Lesson 2-4: Angles and Parallel Lines 12
13 Interior Angles The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. A D L G Line L P Q F B Interior E Line M Line N BPQ + EQP = APQ + DQP = A The pair measures of interior of angles interior lie angles on the in same each side pair of add the up to transversal.
14 Alternate Interior/ Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). 3 6, 4 5 Alternate Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 2 7, Interior
15 Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. L G Line L A D P Q Line M B Line N E F BPQ = DQP APQ = EQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.
16 Parallel Lines w/a transversal AND Angle Pair Relationships Concept Summary Types of angle pairs formed when a transversal cuts two parallel lines. Congruent Supplementary alternate interior angles- AIA same side interior angles- SSI alternate exterior angles- AEA corresponding angles - CA same side exterior angles- SSE linear pair of angles- LP vertical angles- VA
17 Let s Practice m<1=120 Find all the remaining angle measures
18 Parallel Lines and Transversals s t and c d. Name all the angles that are congruent to 1. Give a reason for each answer. s t d c 3 1 corresponding angles 6 1 vertical angles 8 1 alternate exterior angles 9 1 corresponding angles 14 1 alternate exterior angles 1 4 same side exterior angles 5 10 alternate interior angles
19 Another practice problem (40+60)= Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.
20 Name the pairs of the following angles formed by a transversal. Line L G A A 50 0 P P B Line Line M M D D Q E Line Line N N F F
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