![]() ![]() Postulate 1: A line contains at least two points. ![]() Listed below are six postulates and the theorems that can be proven from these postulates. A theorem is a true statement that can be proven. Any straight line segment can be extended indefinitely in a straight. In the definition of right angle, it is clear that the two angles at the foot of a perpendicular, such as angles ACD and BCD, are equal. ![]() Together, these five postulates form the foundation of Euclidean geometry, which is the study of geometry based on Euclid’s axioms. A postulate is a statement that is assumed true without proof. A straight line segment can be drawn joining any two points. The fourth postulate, known as the “parallel postulate,” states that if a straight line intersects two other straight lines and the interior angles on one side of the line add up to less than 180 degrees, then the two lines will eventually intersect on that side.Īlternatively, if the interior angles on one side of the line add up to more than 180 degrees, then the two lines will never intersect. This postulate is crucial in the study of parallel lines and the construction of angles.įinally, the fifth postulate, known as the “Euclidean postulate,” states that if a straight line intersects two other straight lines, and the sum of the interior angles on one side of the line is equal to two right angles, then the two lines will never intersect on that side. This postulate is also crucial in the study of parallel lines and the construction of angles. ![]()
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