Key Points - Lines and Angles

- We recall that
(i)  A line-segment has two end points.
(ii) A ray has only one end point (its vertex); and
(iii) A line has no end points on either side.

- An angle is formed when two lines (or rays or line-segments) meet.

Pairs of Angles - Condition
Two complementary angles - Measures add up to 90°
Two supplementary angles - Measures add up to 180°
Two adjacent angles - Have a common vertex and a common arm but no common interior.

Linear pair
- Adjacent and supplementary

When two lines l and m meet, we say they intersect; the meeting point is called the point of intersection.
-  When lines drawn on a sheet of paper do not meet, however far produced, we call them to be parallel lines.
-  Point: A point name a location.
-  Line: A line is perfectly straight and extends forever in both direction.
-  Line segment: A line segment is the part of a line between two points.
-  Ray: A ray is part of a line that starts at one point and extends forever in one direction.
- Intersecting lines: Two or more lines that have one and only one point in common. The common point where all the intersecting lines meet is called the point of intersection.
- Transversal: A line intersects two or more lines that lie in the same plane in distinct points.
- Parallel lines: Two lines on a plane that never meet. They are always the same distance apart.
- Complementary Angles: Two angles whose measures add to 90° .
- Supplementary Angles: Two angles whose measures add to 180° .
- Adjacent Angles: Two angles have a common vertex and a common arm but no common interior points.
 
- Linear pairs: A pair of adjacent angles whose non-common sides are opposite rays.
- Vertically Opposite Angles: Two angles formed by two intersecting lines have common arm.
- Angles made by Transversal: When two lines are intersecting by a transversal, eight angles are formed.
- Transversal of Parallel Lines: If two parallel lines are intersected by a transversal, each pair of:

- Corresponding angles are congruent.
- Alternate interior angles are congruent.
- Alternate exterior angles are congruent.
If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent to 90° angles.