Chapter 4

C-2      If two angles are a linear pair of angles, then they are supplementary. (Linear Pair Conjecture)

C-3      If two angles are both equal in measure and supplementary, then each angle measures 90.  (Equal Supplements Conjecture)

C-4      The sum of the measures of the three angles of every triangle is 180. (Triangle Sum Conjecture)

C-5      If two angles of one triangle are equal in measure to two angles of another triangle, then the remaining two angles are equal in measure. (Third Angle Conjecture)

C-6      The sum of the measures of the four angles of a quadrilateral is 360.

C-7      The sum of the measures of the n angles of an n-gon is (n - 2)(180). (Polygon Sum Conjecture)

C-8      The measure of each angle of an equiangular n-gon is (n - 2)(180)/n .

C-9      The sum of the measures of one set of exterior angles is 360.

C-10    The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles. (Exterior Angle Conjecture)

C-11    The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (Triangle Inequality Conjecture)

C- 12  In a triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.

C- 13   If a triangle is isosceles, then the base angles are equal in measure . (Isosceles Triangle Conjecture)

C- 14   If a triangle has two angles of equal measure, then the triangle is isosceles. (Converse of the Isosceles Triangle Conjecture)

C- 15   An equilateral triangle is equiangular and, conversely, an equiangular triangle is equilateral. (Equilateral Triangle Conjecture)

C- 16   If two parallel lines are cut by a transversal, then the corresponding angles are equal in measure. Conversely, if two lines are cut by a transversal forming pairs of corresponding angles equal in measure, then the lines are parallel. (CA Conjecture)

C-17    If two parallel lines are cut by a transversal, then the alternate interior angles are equal. Conversely, if two lines are cut by a transversal forming pairs of alternate interior angles equal in measure. then the lines are parallel . (AIA Conjecture)

C-18    If two parallel lines are cut by a transversal, then the alternate exterior angles are equal in measure. Conversely, if two lines are cut by a transversal forming pairs of alternate exterior angles equal in measure, then the lines are parallel. (AEA Conjecture)

C- 19   The base angles of an isosceles trapezoid are equal in measure. (Isosceles Trapezoid Conjecture)

C-20    A midsegment of a triangle is parallel to the third side and one-half the third side. (Triangle Midsegment Conjecture)

C-21    The midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the lengths of the bases. (Trapezoid Midsegment Conjecture)

C-22    The opposite angles of a parallelogram are equal in measure.

C-23    The consecutive angles of a parallelogram are supplementary.

C-24    The opposite sides of a parallelogram are equal in measure.

C-25    The diagonals of a parallelogram bisect each other.

C-26    The diagonals of a rhombus are perpendicular bisectors of each other.

C-27    The diagonals of a rhombus bisect the angles of the rhombus.

C-28    The measure of each angle of a rectangle is 90.

C-29    The diagonals of a rectangle are equal in measure.

C-30    If (x_l, y_l) and (x₂, y₂) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are  ( (x₁ + x₂)/2  ,  (y₁ + y₂)/2  ) (Coordinate Midpoint Conjecture)