Understanding Parallel Lines and Transversals in Plane Geometry
Explore the concept of parallel lines and transversals in plane geometry, including types of angles formed, such as alternate interior angles, alternate exterior angles, and corresponding angles. Learn how to classify angles and find missing angles using these relationships.
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Presentation Transcript
Unit 3 Unit 3- -1 1 Parallel Lines and Parallel Lines and Transversals Transversals PLANE GEOMETRY PLANE GEOMETRY
Transversal: A Line that Intersects 2 or More Coplanar Lines at 2 Distinct Points ? Line ? is a transversal of lines ? and ?. Note that line ? forms 8 angles. ? ?? ? Interior Angles: Lie between lines ? and ?. ?, ?, ?, ? ? ? ?? ?? Exterior Angles: Lie in the two regions that are not between lines ? and ?. ?, ?, ?, ?
Types of Angles: Alternate Interior Angles: Nonadjacent interior angles that lie on opposite sides of transversal ?. ? ? ? Alternate Exterior Angles: Nonadjacent exterior angles that lie on opposite sides of transversal ?. ?? ?? ?? ?? Corresponding Angles: Angles that lie on the same side of transversal ? and on the same side of lines ? and ?. Same-Side Interior Angles (Consecutive Interior Angles): Interior angles that lie on the same side of transversal ?.
Example 1: Classify the given pairs of angles. ? ??? ? ? ??? ? ? ? ? ??? ? ? ??? ? ? ?? ?? ? ??? ? ? ??? ? ?? ? ??? ? ? ??? ? ?? ? ??? ? ? ??? ?
Alternate Interior Angles: If 2 parallel lines are cut by a transversal, then each pair of Alternate Interior Angles is congruent. ? ? ?? ? ? ? ?? ??
Example 2: Find the missing angles. ? ? ? ? ?? ?? ???
Alternate Exterior Angles: If 2 parallel lines are cut by a transversal, then each pair of Alternate Exterior Angles is congruent. ? ? ?? ? ? ? ?? ??
Example 3: Find the missing angles. ? ? ? ? ?? ?? ??
Corresponding Angles: If 2 parallel lines are cut by a transversal, then each pair of Corresponding angles is congruent. ? ? ?? ? ? ? ?? ??
Example 4: Find the missing angle. ? ? ? ??? 11?
Same-Side Interior Angles: If 2 parallel lines are cut by a transversal, then each pair of Same-Side Interior Angles is Supplementary. ? ? ?? ? ? ? ?? ??
Example 5: Find the missing angle. ? ? ? ??? ?
Example 6: Find the missing angles. ? ? = ________ ? ? = ________ ? ? = ________ ? ? = ________ ? ? = ________ ? ? = ________ ? ? = ________ ? ? = ________
