(from the 2nd Edition)

Chapter 3

C-1 If a point is on the perpendicular bisector of a segment, then it is equally distant from the endpoints (Perpendicular Bisector Conjecture). (pg 139)

C-2 If a point is equally distant from the endpoints of a segment, then it is on the perpendicular bisector of the segment (Converse of the Perpendicular Bisector Conjecture). (pg 140)

C-3 The shortest distance from a point to a line is measured along the perpendicular from the point to the line (Shortest Distance Conjecture). (pg 143)

C-4 If a point is on the bisector of an angle, then it is equally distant from the sides of the angle

(Angle Bisector Conjecture). (pg 147)

C-5 The measure of each angle of an equilateral triangle is 60 degrees. (pg 148)

C-6 The three angle bisectors of a triangle are concurrent. (pg 155)

C-7 The three perpendicular bisectors of a triangle are concurrent. (pg 155)

C-8 The three altitudes (or the lines through the altitudes) of a triangle are concurrent. (pg 155)

C-9 The circumcenter of a triangle is equally distant from the triangle's three vertices. (pg 156)

C-10 The incenter of a triangle is equally distant from the triangle's three sides. (pg 156)

C-11 The three medians of a triangle are concurrent. (pg 160)

C-12 The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint. (pg 161)

C-13 The circumcenter, centroid, and the orthocenter are the three points of concurrency that always lie on the Euler line. (pg 162)

C-14 The centroid divides the Euler segment into two parts so that the smaller part is half as long as the larger part. (pg 162)

Chapter 4

C-15 If two angles are vertical angles, then they are congruent (Vertical Angles Conjecture). (pg 174)

C-16 If two angles are a linear pair of angles, then they are supplementary (Linear Pair Conjecture). (pg 175)

C-17 If two parallel lines are cut by a transversal, then corresponding angles are congruent , alternate interior angles are congruent, and alternate exterior angles congruent (Parallel Lines Conjecture). (pg 179)

C-17a If two parallel lines are cut by a transversal, then corresponding angles are congruent (Corresponding Angle Conjecture, or CA Conjecture). (pg 179)

C-17b If two parallel lines are cut by a transversal, then alternate interior angles are congruent (Alternate Interior Angle Conjecture, or AIA Conjecture). (pg 179)

C-17c If two parallel lines are cut by a transversal, then alternate exterior angles are congruent (Alternate Exterior Angle Conjecture, or AEA Conjecture). (pg 179)

C-18 If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, and congruent alternate exterior angles, then the lines are parallel (Converse of the Parallel Lines Conjecture). (pg 180)

C-19 If (X1, Y1,) 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). (pg 187)

C-20 The slope m of a line (or segment) through p1 and p2 with coordinates (X1,Y1)
and (X2, Y2) is given by m = (Y2 - Y1) / (X2 - X1) (Slope of a Line Conjecture) (pg 188)

C-21 In a coordinate plane, two, distinct lines are parallel if and only if their slopes are equal. (Parallel Slope Conjecture). (pg 197)

C-22 In a coordinate plane, two nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other (Perpendicular Slope Conjecture). (pg 198)

C-23 If the grapli of a line has a slope of m and a y-intercept of (0, b), then the equation of the line can be written in the form y= mx + b (Slope-Intercept Conjecture). (pg 201)

C-24 If Triangle TRY has coordinates T(a, d), R(b, e), and Y(c, f) then the centroid has coordinates:
( a + b + c) / 3 , (d + e + f ) / 3 (Centroid Coordinates Conjecture). (pg 209)

Chapter 5

C-25 The sum of the measures of the angles in a triangle is 180 deg. (Triangle Suin Conjecture). (pg 225)

C-26 If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is equal in measure to the third angle in the other triangle (Third Angle Conjecture). (pg 225)

C-27 If a triangle is isosceles, then its? base angles are congruent (Isosceles Triangle Conjecture). (pg 233)

C-28 If a triangle lias two congruent angles, then it is an isosceles triangle (Converse of the Isosceles Triangle Coitjecture). (pg 233)

C-29 An equilateral triangle is equiangular, and, conversely, an equiangular triangle is equilateral (Equilateral Triangle Conjecture). (pg 234)

C-30 The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Conjecture). (pg 238)

C-31 In a triangle, the longest side is opposite the angle with greatest measure and the shortest side is opposite the angle with least measure (Side-Angle Inequality Conjecture). (pg 238)

C-32 The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles (Triangle Exterior Angle Conjecture). (pg 239)

C-33 If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. (SSS Congruence Conjecture). (pg 248)

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 triangles are congruent (SAS Congruence Conjecture). (pg 249)

C-36 If two angles and a side that is not between them in one triangle are congruent to the corresponding two angles and side not between them in another triangle, then the triangles are congruent (SAA Congruence Conjecture). (pg 255)

Chapter 6

C-38 The sum of the measures of the four angles of every quadrilateral is 360' (Quadrilateral Sum Conjecture). (pg 280)

C-39 The sum of the measures of the n angles of an n-gon is 180 (n - 2) (Polygon Sum Conjecture). (pg 28 1)

C-40 The sum of the measures of one set of exterior angles is 360 deg. (Exterior Angle Sum Conjecture). (pg 28

C-41 The measure of each angle of an equiangular n-gon can be found by using the following expressions: (n - 2)180 / n (Equiangular Polygon Conjecture). (pg 285)

C-42 The diagonals of a kite are perpendicular (Kite Diagonals Conjecture). (pg 289)

C-43 The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal (Kite Diagonal Bisector Conjecture). (pg 290)

C-44 The nonvertex angles of a kite are congruent (Kite Angles Conjecture). (pg 290)

C-45 The vertex angles of a kite are bisected by a diagonal (Kite Angle Bisector Conjecture). (pg 290)

C-46 The consecutive angles between the bases of a trapezoid are supplementary (Trapezoid Consecutive Angles Conjecture). (pg 291)

C-47 The base angles of an isosceles trapezoid are congruent (Isosceles Trapezoid Conjecture). (pg 291)

C-48 The diagonals of an isosceles trapezoid are congruent (Isosceles Trapezoid Diagonals Conjecture).(pg 291)

C-49 The three midsegments of a triangle divide the triangle into four congruent triangles. (pg 297)

C-50 A midsegment of a triangle is parallel to the third side and half the length of the third side (Triangle Midsegment Conjecture) (pg 297)