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segment addition postulate AB + BC = AC Linear Pair Postulate m<1 + m<2= 180 degrees Vertical Angles Theorem If two angles intersect to form an X, the non adjacent angles are congruent Angle Addition Postulate if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC syllogism p -> q, and q -> r, then p -> r Detatchment p -> q, p is true than q is true Congruent Supplements Theorem if m<1 + m<2=180, and m<2 + m<3 = 180, then m<1 + m<3 = 180. Congruent Complements Theorem if m<4 + m<5 = 90, and m<5 + m<6 = 90, then m<4 + m<6 = 90. reflexive property a=a Symmetric Property ab=ba Transitive Property ab=cd, cd=ef, then ab=ef 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 lines 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 Theorem 3.3 If two lines are perpendicular, then they intersect to for 4 right angles Alternate interior angles theorem if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent Consecutive Interior Angles theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary Corresponding angles postulate if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent Alternate exterior angles postulate if two lines cut by a transversal are parallel, then alternate exterior angles are congruent Triangle Sum theorem The 3 interior angles of a triangle add up to 180 degrees Exterior angles 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 Propery (Triangles) Every triangle is congruent to itself Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other Base angles theorem (Converse) If 2 <s of a Δ are ≅, then the 2 sides opposite are ≅ Postulate/Slopes of Perpendicular Lines Two lines are perpendicular is and only if the product of the slope is -1 Side Side Side 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 Postulate If two sides and an included angle of one triangle are congruent to two sides and an included angle of a second triangle, then the two triangles are congruent Angle Side Angle Postulate If two angles and an included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent Theorem 3.2 If two sides of two adjacent acute angles are perpendicular, then the angles are complementary Theorem 3.3 If two lines are perpendicular, then they intersect to form 4 right angles Perpendicular Travsversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other Theorem 3.11 If two lines are parallel to the same line, then they are parallel to eachother Theorem 3.12 In a plane, if two lines are perpendicular to the same line, then they are parallel to eachother Collorary to the triangle sum theorem the acute angles of a triangle are complementary Converse of the base angles theorem If two angles of a triangle are congruent, then the sides opposite them are congruent Collorary of the converse of the base angles theorem If a triangle is equiangular then it is also equilateral Hypotenuse-Leg Theorem If they hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then those two triangles are congruent