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Postulate 1-1-1 Through any two points there is exactly one line. Postulate 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Postulate 1-1-3 If two points lie in a plane, then the line containing those points lies in the plane. Postulate 1-1-4 If two lines intersect, then they intersect in exactly one point. Postulate 1-1-5 If two planes intersect, then they intersect in exactly one line. Postulate 1-2-1 Ruler Postulate The points on a line can be put in a one-to-one correspondence with the real numbers. Postulate 1-2-2 Segment Addition Postulate If B is between A and C, then AB + BC = AC Postulate 1-3-1 Protractor Postulate Given line AB and a point O on line AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180. Postulate 1-3-2 Angle Addition Postulate If S is in the interior of angle PQR, then the measure of angle PQS + the measure of angle SQR = the measure of angle PQR. Postulate 3-2-1 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Postulate 3-3-1 Converse of the Corresponding Angles Postulate If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. Postulate 3-3-2 Parallel Postulate Through a point P not on line l, there is exactly one line parallel to l. Corollary 4-2-2 The acute angles of a right triangle are complementary. Corollary 4-2-3 The measure of each angle of an equiangular triangle is 60°. Postulate 4-4-1 Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Postulate 4-4-2 Side-Angle-Side Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the the triangles are congruent. Postulate 4-5-1 Angle-Side-Angle Congruence Postulate If two angles and the included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent. Corollary 4-8-3 If a triangle is equilateral, then it is equiangular. Corollary 4-8-4 If a triangle is equiangular, then it is equilateral. Postulate 7-3-1 Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Corollary 7-4-3 Two-Transversal Proportionality Corollary If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. Corollary 8-1-2 Geometric Means Corollary The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse Corollary 8-1-3 Geometric Means Corollary The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg. Postulate 9-1-1 Area Addition Postulate The area of a region is equal to the sum of the areas of its nonoverlapping parts. Postulate 11-2-1 Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. Corollary 11-4-2 If inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc, then the angles are congruent.