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51 Cards in this Set

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 Segment Addition Postulate If B is between A and C,then AB+BC=AC. If AB+BC=AC, then B is between A and C. Angle Addition Postulate If P is in the interior of ∠RST, then m∠RSP+m∠PST=m∠RST. N/A Through any two points there exists exactly one line. N/A A line contains at least two points. N/A If two lines intersect, then their intersection is exactly one point. N/A Through any three noncollinear points there exists exactly one plane. N/A A plane contains at least three noncollinear points. N/A If two points lie in a plane, then the line containing them lies in the plane. N/A If two planes intersect, then their intersection is a line. Linear Pair Postulate If two angles form a linear pair, then they are supplementary. Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding Angles Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Slopes of Parallel Lines In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular. Side-Side-Side Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Side-Angle-Side Congruence Postulate If two sides and the included side of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. Angles-Side-Angle Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. Area of a Square Postulate The area of a square is the square of the length of its side, or A=s². Area Congruence Postulate If two polygons are congruent,then they have the same area. Area Addition Postulate The area of a region is the sum of the areas of its nonoverlapping parts. Angle-Angle Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. Volume of a Cube The volume of a cube is the cube of the length of its side. Volume Congruence Postulate If two polyhedra are congruent, then they have the same volume. Volume Addition Postulate The volume of a solid is the sum of the volumes of all its nonoverlapping parts. Properties of Segment Congruence Segment congruence is reflexive, symmetric, and transitive. Properties of Angle Congruence Angle congruence is reflexive, symmetric, and transitive. Right Angle Congruence Theorem All right angles are congruent. Congruent Supplements Theorem If two angles are supplementary to the same angle then they are congruent. Congruent Supplements Theorem If two angles are complementary to the same angle then the two angles are congruent. Vertical Angles Theorem Vertical angles are congruent. N/A If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. N/A If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. N/A If two lines are perpendicular, then they intersect to form four right angles. Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Alternate Interior Angles Converse If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. Consecutive Interior Angles Converse If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Alternate Interior Angle Converse If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. N/A If two lines are parallel to the same line, then they are parallel to each other. N/A In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°. Exterior Angle Theorem the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Reflexive Property of Congruent Triangles Every triangle is congruent to itself. Symmetric Property of Congruent Triangles If △ABC congruent △DEF, then △DEF congruent △ABC Transitive Property of Congruent Triangles If △ABC congruent △DEF and △DEF congruent △JKL, then △ABC congruent △JKL.