Synthetic Geometry

1. Synthetic Geometry Leaving Certificate Higher Level Mathematics

2. Planes and Points • A plane is a flat surface that goes on for infinity in all directions. • A point is a precise location on the plane. Usually represented by a dot. We denote points with capital letters.i.e. A,B,C etc • A line is a geometrical object that is straight, infinitely long and infinitely thin. We denote lines with lower case letters. i.e. a,b,c etc • A line segment is a straight line which links too points without extending beyond them. Can be measured using a ruler. • A ray is a portion of a line which starts at a point and goes off in a particular direction to infinity. • Collinear points are a set of points that lie on a straight line.

3. Axiom 1-Two Points Axiom • There is exactly one line through any two given points.

4. Axiom 2: Ruler Axiom • The distance between points has the following properties: • The distance |AB| is never negative • |AB| = |BA| • If C lies on AB,between A and B, then |AB| = |AC| + |CB| • Given any ray from A, and given any real number k≥ 0,there is a unique point B on the ray whose distance from A is k

5. Axiom 3- Protractor Axiom • The number of degrees in an angle is always a number between O° and 360°. The number of degrees in an ordinary angle is less than 180°. It has these properties: • A straight angle has 180° • If D is a point inside an angle ∟BAC then |∟BAC|= |∟BAD| + |∟DAC| |∟BAD| + |∟DAC| are called supplementary angles i.e. they add up to 180°

6. Axiom 3- Protractor Axiom