then every point of a lies in α. In this case we say: "The line a lies in the plane α", etc. If two planes α, β have a point A in common, then they have at least a second point B in common. There exist at least four points not lying in a plane. II. Order If a point B lies between points A and C, B is also between C and A, and there exists a line containing the distinct points A, B, C. If A and C are two points, then there exists at least one point B on the line AC such that C lies between A and B. Of any three points situated on a line, there is no more than one which lies between the other two. Pasch's Axiom: Let A, B, C be three points not lying in the same line and let a be a line lying in the plane ABC and not passing through any of the points A, B, C. Then, if the line a passes through a point of the segment AB, it will also pass through either a point of the segment BC or a point of the segment AC. III. Congruence If A, B are two points on a line a, and if A′ is a point upon the same or another line a′, then, upon a given side of A′ on the straight line a′, we can always find a point B′ so that the segment AB is congruent to the segment A′B′. We indicate this relation by writing . Every segment is congruent to itself; that is, we always have .We can state the above axiom briefly by saying that every segment can be laid off upon a given side of a given point of a given straight line in at least one way. If a segment AB is congruent to the segment A′B′ and also to the segment A″B″, then the segment A′B′ is congruent to the segment A″B″; that is, if and , then . Let AB and BC be two segments of a line a which have no points in common aside from the point B, and, furthermore, let A′B′ and B′C′ be two segments of the same or of another line a′ having, likewise, no point other than B′ in common. Then, if and , we have . Let an angle