Lines and Angles
G.CO.1 Know precise definitions of perpendicular line and parallel lines, based on the undefined notions of point, etc.
Goals for this section:
Students should be able to identify what a transversal is and what interior, exterior, alternate, same-side, and corresponding mean in relation to lines being intersected by a transversal.
Parallel and Skew
Parallel Lines are on the same plane (coplanar) and do not intersect. The symbol || means parallel.
Skew lines are not coplanar, not parallel, and do not intersect.
Think of each side of the cube as a plane.
- A || B since it's on the same plane and they do not intersect.
- C and D are skew because they are not on the same plane, they do not intersect, and they are not parallel.
Transversal
A transversal is a line that intersects two lines that are on the same plane. The red lines represent a transversal.
Interior and Exterior
Interior
The highlighted portion is on the inside, which is interior.
Exterior
The highlighted portions are on the outside, which is exterior.
Angle Pairs formed by Transversals
∠1 is alternate interior to ∠3
∠2 is alternate interior to ∠4
Alternate Interior Angles
These angles are on the inside. Alternate means to be on different sides of the transversal. Think of alternate as switching sides.
∠1 is same-side interior to ∠4
∠2 is same-side interior to ∠3
Same-Side Interior Angles
These angles are on the inside. Same-side is what it sounds like. They're on the same side of the transversal.
∠1 is corresponding to ∠5
∠2 is corresponding to ∠6
∠3 is corresponding to ∠7
∠4 is corresponding to ∠8
Corresponding Angles
These angles are on the same side of the transversal and in corresponding positions.
Notice how when the transversal intersects a line it creates a group of four angles. There's a top left, top right, bottom left, and bottom right angle. So corresponding angles have to have matching relative "positions".
∠1 is alternate exterior to ∠4
∠2 is alternate exterior to ∠3
Alternate Exterior Angles
These angles are on the outside. They're also on alternate sides of the transversal, or else they have switched sides.
