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Theorems: POINTS, LINES, PLANES, AND ANGLESTheorem 1-1: If two lines intersect, then they intersect in exactly one point.Theorem 1-2: Through a line and a point not in the line, there is exactly one plane.Theorem 1-3: If two lines intersect, then exactly one plane contains the lines.

DEDUCTIVE REASONINGTheorem 2-1: (Midpoint Theorem)- If M is the midpoint of AB, then AM = AB and MB = AB.Theorem 2-2: (Angle Bisector Theorem)- If BX is the bisector of angle ABC, then ABX = ABCand XBC = ABC.Theorem 2-3: Vertical angles are congruent.Theorem 2-4: If two lines are perpendicular, then they form congruent adjacent angles.Theorem 2-5: If two lines form congruent adjacent angles, then the lines are perpendicular.Theorem 2-6: If the exterior sides of two adjacent acute angles are perpendicular, then theangles are complementary.Theorem 2-7: If two angles are supplements of congruent angles (or of the same angle), thenthe two angles are congruent.Theorem 2-8: If two angles are complements of congruent angles (or of the same angle), thenthe two angles are congruent.

PARALLEL LINES AND PLANESTheorem 3-1: If two parallel planes are cut by a third plane, then the lines of intersection areparallel.Theorem 3-2: If two parallel lines are cut by a transversal, then AIA are congruent.Theorem 3-3: If two parallel lines are cut by a transversal, then SSI angles are supplementary.Theorem 3-4: If a transversal is perpendicular to one of two parallel lines, then it isperpendicular to the other line as well.Theorem 3-5: Two lines are cut by a transversal and the AIA are congruent, then the lines areparallel.

Theorem 3-6: If two lines are cut by a transversal and SSI angles are supplementary then thelines are parallel.Theorem 3-7: In a plane two lines perpendicular to the same line are parallel.Theorem 3-8: Through a point outside a line, there is exactly one parallel to the given line.Theorem 3-9: Through a point outside a line, there is exactly one perpendicular to the givenline.Theorem 3-10: Two lines parallel to a third line are parallel to each other.Theorem 3-11: The sum of the measures of the angles of a triangle is 180 degrees.C 1: If two angles of one triangle are congruent to two angles of another triangle, thenthe third angles are congruent.C 2: Each angle of an equiangular triangle has a measure of 60 degrees.C 3: In a triangle, there can be at most one right angle or obtuse angle.C 4: The acute angles of a right triangle are complementary.Theorem 3-12: The measure of an exterior angle of a triangle equals the sum of the measures

of the two remote interior angles.Theorem 3-13: The sum of the measures of the angles of a convex polygon withn sides is (n-2)180.Theorem 3-14: The sum of the measures of the exterior angles of any convex polygon, oneangle at each vertex, is 360 degrees.

CONGRUENT TRIANGLESTheorem 4-1: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.C 1: An equilateral triangle is also equiangular.C 2: An equilateral triangle has three 60 degree angles.C 3: The bisector of the vertex angle of an isosceles triangle is perpendicular to thebase at its midpoint.Theorem 4-2: Converse of theorem 4-1.Theorem 4-3: AAS; if two angles and a non-included side of one triangle are congruent to the

corresponding parts of another right triangle, then they are congruent.Theorem 4-4: HL; if the hypotenuse and a leg on a right triangle, are congruent to that of another, then the two triangles are congruent.Theorem 4-5: If a point lies on the perpendicular bisector of a segment, then the point isequidistant from both ends of the segment.Theorem 4-6: Converse of theorem 4-5.Theorem 4-7: If a point is equidistant from the endpoints of a segment, then the point isequidistant from the sides of the angle.Theorem 4-8: If a point is equidistant from the sides of an angle, then the point lies on thebisector of the angle.

QUADRILATERALSTheorem 5-1: Opposite sides of a parallelogram are congruentTheorem 5-2: Opposite angles of a parallelogram are congruent.Theorem 5-3: Diagonals of a parallelogram bisect each other.Theorem 5-4: If both pairs of opposite sides of a quadrilateral are congruent, then it is aparallelogram.Theorem 5-5: If one pair of opposite sides is both congruent and parallel, then the quadrilateralis a parallelogram.Theorem 5-6: If both pairs of opposite angles of a quadrilateral are congruent, then it is aparallelogram.Theorem 5-7: If the diagonals of a parallelogram bisect each other, then the quadrilateral is aparallelogram.Theorem 5-8: If two lines are parallel, then all points on one line are equidistant from the other

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line.Theorem 5-9: If three parallel lines are cut off into congruent segments on one transversal,then they cut off congruent segments in every transversal.Theorem 5-10: A line that contains the midpoint of one side of a triangle and is parallel toanother side passes thought the midpoint of the third side.Theorem 5-11: The segment that joins the midpoints of two sides of a triangle (1) is parallel tothe third side (2) is half as long as the third side.Theorem 5-12: The diagonals of a rectangle are congruent.Theorem 5-13: The diagonals of a rhombus are perpendicular.Theorem 5-14: Each diagonal of a rhombus bisects two angles of the rhombus.Theorem 5-15: The midpoint of the hypotenuse of aright triangle is equidistant from the threevertices.Theorem 5-16: If an angle of a parallelogram is a right angle, the parallelogram is a rectangle.Theorem 5-17: If two consecutive sides of a parallelogram are congruent, then theparallelogram is a rhombus.Theorem 5-18: Base angles of an isosceles trapezoid are congruent.Theorem 5-19: The median of a trapezoid (1) Is parallel to the bases (2) has a length equal tothe average of the base lengths.