Angles and lines
Last updated: 15 Nov 2008
Angles
All angles in the GMAT are measured in degrees and there are 360° in a full circle.
Crossing lines
When two lines cross they form two pairs of angles. The angles opposite each other are equal and angles next to each other add up to a straight line, i.e. 180°.
Therefore, in the diagram above, the two angles marked x are equal, the two angles marked y are equal and finally x + y = 180°.
Parallel lines
Parallel lines, on a plane, are those which never cross. They are always the same distance apart however far you extend them. The symbol < is often used to show that two lines are parallel.
If a line crosses two parallel lines then it will form two sets of four equal angles, see the diagram below.
All angles marked x are equal and all angles marked y are equal.
Perpendicular lines
Lines which meet at right angles, i.e. 90°, are perpendicular lines.
I leave it as an excercise for you to work out why all four angles in this diagram are right angles (using what you have already learned about crossing lines).
Contents
- Introduction
- Geometry tips
- Angles and lines
- Triangles
- The Pythagoras theorem
- Common triangles
- Common quadrilaterals
- The trapezium
- Circles, sectors and arcs
- Cuboids and cylinders
- Coordinate geometry
- Summary of geometry
Practice questions
