Planes and Lines the Concepts of Parallel Skew

Planes and Lines: the Concepts of Parallel, Skew and Transversal Section 3. 1 Big Ideas Geometry

Definition of Parallel Lines � Parallel Lines: Two lines that do not intersect and are coplanar ◦ The symbol for parallel is || and is read “is parallel to”. So m||n reads “line m is parallel to line n” m n

Definition of Skew Lines and Parallel Planes � Skew Lines: Two lines that do not intersect but are not coplanar � Parallel Planes: Two planes that do not intersect each other

From Unit 1 � Perpendicular a 90° angle Lines: two lines that intersect at ◦ The symbol for perpendicular is ⊥ and is read “is perpendicular to”. So m⊥n is read “line m is perpendicular to line n”. m n

The Parallel and Perpendicular Postulate � Parallel Postulate: If there is a line and a point not on that line, then there is exactly one line through the point parallel to the given line p n m

The Parallel and Perpendicular Postulate � Perpendicular Postulate: If there is a line and a point not on that line, then there is exactly one line through the point perpendicular to the given line m n p

The Transversal Line � Transversal Line: a line that intersects two or more coplanar lines at different points ◦ We say that t is transversal to lines m and n t 1 3 2 n 4 5 6 7 8 m

4 Pairs of Angles � 1. Corresponding Angles: two angles that have corresponding positions. In the diagram, ∠ 2 and ∠ 6 are corresponding angles since each is above its respective line and to the right of transversal t ◦ ∠ 1 and ∠ 5, ∠ 3 and ∠ 7, ∠ 4 and ∠ 8 are the other three corresponding angle pairs

4 Pairs of Angles � 2. Alternate Interior Angles: two angles that lie in between the two lines and on opposite sides of the transversal t ◦ ∠ 3 and ∠ 6, ∠ 4 and ∠ 5 are the alternate interior angle pairs

4 Pairs of Angles � 3. Alternate Exterior Angles: two angles that lie outside the two lines and on opposite sides of the transversal t ◦ ∠ 1 and ∠ 8, ∠ 2 and ∠ 7 are the alternate exterior angle pairs

4 Pairs of Angles � 4. Consecutive Interior Angles: two angles that lie between the two lines and on the same side of the transversal t ◦ ∠ 3 and ∠ 5, ∠ 4 and ∠ 6 are the consecutive interior angle pairs

Bibliography � https: //www. jackson. stark. k 12. oh. us/site/ha ndlers/filedownload. ashx? moduleinstanceid= 371&dataid=1941&File. Name=geometry%20 le sson%203 -1. pdf � Google Maps