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 (xl, yl) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are ( (xl + x2)/2 , (yl + y2)/2 ) (Coordinate Midpoint Conjecture)
C-31 In a coordinate plane, two lines are parallel if and only if their slopes are =. (Parallel Slope Conjecture)
C-32 In a coordinate plane, two lines are perpendicular if and only if their slopes are the negative reciprocals of each other. (Perpendicular Slope Conjecture)
Chapter 5
C-33 If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. (SSS Congruence Conjecture)
C-34 If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the two triangles are congruent. (SAS Congruence Conjecture)
C-35 If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent. (ASA Congruence Conjecture)
C-36 If two angles and a side that is not between them in one triangle are congruent to two angles and a side that is not between them in another triangle, then the two triangles are congruent. (SAA Congruence Conjecture)
C-37 In an isosceles triangle, the bisector of the vertex angle is also the altitude to the base and the median to the base. (Vertex Angle Conjecture)
Chapter 6
C-38 If two chords in a circle are congruent,
then they determine two central angles that are
congruent.
C-39 If two chords in a circle are congruent, then their intercepted arcs are congruent.
C-40 Two congruent chords in a circle are equally distant from the center of the circle.
C-41 The perpendicular bisector of a chord passes through the center of the circle.
C-42 A tangent to a circle is perpendicular to the radius drawn to the point of tangency. (Tangent Conjecture)
C-43 Tangent segments to a circle from a point outside the circle are congruent. (Tangent Segments Conjecture)
C-44 The measure of an inscribed angle in a circle equals one-half the measure of its intercepted arc. (Inscribed Angle Conjecture)
C-45 Angles inscribed in the same arc are congruent.
C-46 Every angle inscribed in a semicircle is a right angle.
C-47 The opposite angles of a quadrilateral inscribed in a circle are supplementary.
C-48 Parallel lines intercept congruent arcs on a circle.
C-49 If C is the circumference and D is the diameter of a circle, then there is a number p such that C = pD . Since D = 2r where r is the radius, the C = 2pr.
C-50 The arc length equals the arc measure divided by 360, times the circumference of the circle.