Conjecture and Guess may not be used to justify the steps of a proof. A conjecture is based on prediction only. Because these are only predictions, they cannot be guaranteed accurate. A guess cannot be used as it’s exactly what it says; a guess, and once again, may or may not be true.

Postulates are accepted without proof as that is the rule, so are without doubt considered proof. Their purpose is to explain the terms and to serve as the starting point for proving other statements. The following are different kinds of Postulates:

Point-Line-Plane Postulate; Unique Line Assumption: With any two points there is exactly one line.

Dimension Assumption: Assuming a line is a plane, the point in the plane is not in the line, and a plane in space, is the line in space not on the plane. Number Line Assumption: Every line has a set of points that can be corresponded with numbers with any point corresponding to zero and any other point corresponding to one. Distance Assumption: There is a unique distance between two points. Two points that lie on a plane and the line containing them lies on the plane as well.

Euclid's Postulates: Two points determine a line. A line segment can be extended in along a line. A circle can be drawn with a centre at any radius. All right angles are congruent.

Polygon Inequality Postulates:

Triangle Inequality Postulate: The total of the lengths of two sides of a triangle is more than the length of the third side of a triangle.

Quadrilateral Inequality Postulate: The total lengths of the thre sides of any quadrilateral are more than the length of the fourth side.

A theorem is a proven theory (hence theorem) and has support to back it up.

Euclid's First Theorem, Line Intersection Theorem: Two different lines intersect in at most one point.

The Betweenness Theorem: If C is between A and B and on AB, then AC + CB = AB.

Pythagorean Theorem: A2 + b2 = c2 if c is the hypotenuse.

Right Angle Congruence Theorem: All right angles are congruent.

Postulates are accepted without proof as that is the rule, so are without doubt considered proof. Their purpose is to explain the terms and to serve as the starting point for proving other statements. The following are different kinds of Postulates:

Point-Line-Plane Postulate; Unique Line Assumption: With any two points there is exactly one line.

Dimension Assumption: Assuming a line is a plane, the point in the plane is not in the line, and a plane in space, is the line in space not on the plane. Number Line Assumption: Every line has a set of points that can be corresponded with numbers with any point corresponding to zero and any other point corresponding to one. Distance Assumption: There is a unique distance between two points. Two points that lie on a plane and the line containing them lies on the plane as well.

Euclid's Postulates: Two points determine a line. A line segment can be extended in along a line. A circle can be drawn with a centre at any radius. All right angles are congruent.

Polygon Inequality Postulates:

Triangle Inequality Postulate: The total of the lengths of two sides of a triangle is more than the length of the third side of a triangle.

Quadrilateral Inequality Postulate: The total lengths of the thre sides of any quadrilateral are more than the length of the fourth side.

A theorem is a proven theory (hence theorem) and has support to back it up.

Euclid's First Theorem, Line Intersection Theorem: Two different lines intersect in at most one point.

The Betweenness Theorem: If C is between A and B and on AB, then AC + CB = AB.

Pythagorean Theorem: A2 + b2 = c2 if c is the hypotenuse.

Right Angle Congruence Theorem: All right angles are congruent.