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Axioms

Axioms. A rule or a statement which we accept without any proof. Draw 2 points. Draw lines between these 2 points. How many can you draw? Axiom 1 : there is exactly one line through any 2 points. Ruler axiom. Draw a line between 2 points A and B. Measure from A to B and measure from B to A

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Axioms

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  1. Axioms • A rule or a statement which we accept without any proof. • Draw 2 points. Draw lines between these 2 points. How many can you draw? Axiom 1 : there is exactly one line through any 2 points.

  2. Ruler axiom • Draw a line between 2 points A and B. • Measure from A to B and measure from B to A • Draw a point C on the line AB. Measure from A to C and from C to B.

  3. Ruler axiom Cont. • From the previous procedure you will find the following to be true: Axiom 2: • Distance is never negative. • The distance from A to B is the same as from B to A and • The distance from A to C added to the distance from C to B = the distance from A to B

  4. Protractor axiom These are the properties of the degree measure of an angle. Axiom 3 • A straight angle has an angle of 180o • A null angle is 0o • A right angle is 90o

  5. Congruent triangles • Axiom 4 • Triangles are congruent ( equal ) if they satisfy one of the following 4 conditions, • SSS = 3 sides equal • SAS = side angle side equal • ASA = angle side angle equal • RHS = right angle, hypotenuse and side equal

  6. Axiom of parallels • Draw a line. Call it L. Draw a point P. draw a line through P parallel to L. how many can you draw? • Axiom 5 • There is only one line you can draw through a point P that is parallel to L

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