Plane Geometry: Points, Lines and Angles
Plane geometry studies figures on a flat surface. Points, lines, segments, circles and angles provide the language for describing shapes.
Points and lines
A point shows an exact position. A line extends indefinitely in both directions; a line segment has two endpoints; a ray has one endpoint. Parallel lines never meet, while perpendicular lines meet at 90°. The midpoint divides a segment into two equal parts.
Circles
A circle is the set of points at a fixed distance from a centre. The radius joins the centre to the circumference, the diameter passes through the centre and equals 2r, and a chord joins two points on the circumference.
Angles
An angle is formed by two rays with a common vertex. Acute angles are less than 90°, right angles equal 90°, obtuse angles lie between 90° and 180°, straight angles equal 180° and reflex angles lie between 180° and 360°. Complementary angles sum to 90°; supplementary angles sum to 180°.
Worked examples and practice
- The complement of 37° is 90° − 37° = 53°.
- The supplement of 118° is 180° − 118° = 62°.
- A segment from (not drawn) endpoints of equal distance has its midpoint halfway along the length.
- Classify 45°, 90°, 135° and 270°. State the relationship between parallel and perpendicular lines.
