Conjectures


Chapter 2
C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180°. (Lesson 2.5)
C-2 Vertical Angles Conjecture If two angles are vertical angles, then they are congruent (have equal measures). (Lesson 2.5)
C-3a Corresponding Angles Conjecture, or CA Conjecture If two parallel lines are cut by a transversal, then corresponding angles are congruent. (Lesson 2.6)
C-3b Alternate Interior Angles Conjecture, or AlA Conjecture If two parallel lines are cut by a transversal, then alternate interior angles are congruent. (Lesson 2.6)
C-3c Alternate Exterior Angles Conjecture, or AEA Conjecture If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. (Lesson 2.6)
C-3 Parallel Lines Conjecture If two parallel lines are cut by a transversal, then
corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent. (Lesson 2.6)
C-4 Converse of the Parallel Lines Conjecture If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are parallel. (Lesson 2.6)

 

Chapter 3
C-5 Perpendicular Bisector Conjecture If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints. (Lesson 3.2)
C-6 Converse of the Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. (Lesson 3.2)
C-7 Shortest Distance Conjecture The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line. (Lesson 3.3)
C-8 Angle Bisector Conjecture If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. (Lesson 3.4)
C-9 Angle Bisector Concurrency Conjecture The three angle bisectors of a triangle are concurrent (meet at a point). (Lesson 3.7)
C-10 Perpendicular Bisector Concurrency Conjecture The three perpendicular bisectors of a triangle are concurrent. (Lesson 3.7)
C-11 Altitude Concurrency Conjecture The three altitudes (or the lines containing the altitudes) of a triangle are concurrent. (Lesson 3.7)
C-12 Circumcenter Conjecture The circumcenter of a triangle is equidistant from the vertices. (Lesson 3.7)
C-13 Incenter Conjecture The incenter of a triangle is equidistant from the sides. (Lesson 3.7)
C-14 Median Concurrency Conjecture The three medians of a triangle are concurrent. (Lesson 3.8)
C-15 Centroid Conjecture 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 of the opposite side. (Lesson 3.8)
C-16 Center of Gravity Conjecture The centroid of a triangle is the center of gravity of the triangular region. (Lesson 3.8)

 

Chapter 4
C-17 Triangle Sum Conjecture The sum of the measures of the angles in every triangle is 180°. (Lesson 4.1)
C-18 Third Angle Conjecture 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. (Lesson 4.1)
C-19 Isosceles Triangle Conjecture If a triangle is isosceles, then its base angles are congruent. (Lesson 4.2)
C-20 Converse of the Isosceles Triangle Conjecture If a triangle has two congruent angles, then it is an isosceles triangle. (Lesson 4.2)
C-21 Triangle Inequality Conjecture The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (Lesson 4.3)
C-22 Side-Angle Inequality Conjecture In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. (Lesson 4.3)
C-23 Triangle Exterior Angle Conjecture The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. (Lesson 4.3)