Intersection – the set of points two figures have in common
If two lines intersects, their intersection is a single point.
If two lines intersect, then they are either perpendicular or oblique.
Perpendicular lines – lines that intersect to form a right angle
Oblique lines – lines that intersect that are not perpendicular.
If two lines do not intersect, then they are either parallel or skew.
Parallel lines – coplanar lines that do not intersect
Skew lines – non-coplanar lines that do not intersect
Transversal – a line that intersects two or more coplanar lines at different points
Line t is a transversal. It intersects lines a and b at different points. The transversal creates two angle clusters.
What kind of angles are ∠1 and ∠3? What kind of angles are ∠6 and ∠7?
Interior versus Exterior angles…
Alternate verses Same-side angles…
Alternate interior angles – two non-adjacent interior angles on opposite sides of the transversal
∠3 and ∠5 are alternate interior angles. Which other pair of angles are alternate interior angles?
∠5 and ∠6 are not alternate interior angles. Why?
Alternate exterior angles – two non-adjacent exterior angles on opposite sides of the transversal
∠1 and ∠7 are alternate exterior angles. Which other pair of angles are alternate exterior angles?
∠7 and ∠8 are not alternate exterior angles. Why?
Same-side interior angles – two non-adjacent interior angles on the same side of the transversal
∠4 and ∠5 are same side interior angles. Which other pair of angles are same side interior?
Same-side exterior angles -
Name 2 pairs of same-side exterior angles.
Corresponding angles – two non-adjacent angles on the same side of the transversal such that one angle is an interior angle and the other is an exterior angle.
∠1 and ∠5 are corresponding angles. Notice how the two angles are in the same positions. Both angles are in the top left position in each angle cluster. Corresponding angles will have location in common.
Name 3 other pairs of corresponding angles.