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Geometry unit 3.1.3.3
This document provides information about parallel lines and transversals. It defines key terms like parallel lines, transversals, interior and exterior angles. It describes angle relationships that exist between parallel lines cut by a transversal, such as corresponding angles being congruent, alternate interior angles being congruent, same side interior angles being supplementary. Examples are provided to illustrate these concepts and properties. The document also discusses using these properties to find missing angle measures.
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Definition of parallel lines and non-parallel lines with symbols; arrows indicate parallelism.
Explanation of a transversal line intersecting multiple lines, with reference to non-parallel lines.
Concept of interior and exterior spaces created by two lines, clarifying their definitions.
Types of angles formed, such as alternating and same-side angles, and their properties when lines are parallel.
Definition and congruency of corresponding angles formed by a transversal intersecting parallel lines.
Discussions on same-side angles, their measures, and properties regarding interior and exterior angles.
Definition and properties of alternate interior and exterior angles formed by transversals.
Problem-solving for angle measures using given degrees and related postulates or theorems.
Legal notice regarding copyright and fair use in educational contexts.
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Geometry unit 3.1.3.3
- 2. What would youcall two lines which do not intersect? A B D C Parallel 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 Interior Exterior Exterior
- 3. A slash throughthe parallel symbol || indicates the lines are not parallel. A D B C AB || CD
- 4. A line, ray,or segment that intersects 2 or more COPLANAR lines, rays, or segments. Parallel lines transversal Non-Parallel lines transversal Exterior Interior Exterior Interior Exterior Exterior
- 5. A transversal isa line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. t Transversal - j k m 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 spaceINSIDE the 2 lines interior EXTERIOR -The space OUTSIDE the 2 lines exterior exterior
- 7. 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 1 4 2 3 6 Exterior 5 7 8 Exterior Angles <1 & <8 are Alternate Exterior angles <2 & <7 are Alternate Exterior angles <1 & <7 are Same Side Exterior angles <2 & <8 are Same Side Exterior angles Interior Exterior
- 8. ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY 1 4 2 3 Exterior Interior 5 6 7 8 Exterior If the lines are not parallel, these angle relationships DO NOT EXIST.
- 9. Corresponding Angles: Twoangles that occupy corresponding positions. 2 6, 1 5, 3 7, 4 8 Exterior 1 2 3 4 5 6 7 8 Interior Exterior
- 10. Corresponding Angles Whentwo parallel lines are cut by a transversal, pairs of corresponding angles are formed. GPB = PQE GPA = PQD BPQ = EQF APQ = DQF Line M A B Line N D E Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent. L P Q G F Line L
- 11. Same Side InteriorAngles: Two angles that lie between parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m1 +m7 = 180º, m2 +m8 = 180º 1 2 3 4 5 6 7 8 Exterior Interior Exterior
- 12. Interior Angles Theangles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. Line M L Line L P G Exterior A B Line N 600 1200 600 Q 1200 Interior D E F BPQ + EQP = 1800 APQ + DQP = 1800 Exterior The measures of interior angles in each pair add up to 1800. A pair of interior angles lie on the same side of the transversal.
- 13. Alternate InteriorAngles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). 3 6, 4 5 Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 2 7, 1 8 1 2 3 4 5 6 7 8 Exterior Interior Exterior
- 14. Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M L P G A B Line N Q D E F Line L BPQ = DQP APQ = EQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.
- 15. m<1=120° Find allthe remaining angle measures. 1 4 2 3 5 6 7 8 60° 60° 60° 60° 120° 120° 120° 120°
- 16. Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 120° 60° 120° 60° 40° 60° 60° 180-(40+60)= 80° 80° 80° 100° 80° 100°
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