Conjectures

Conjectures

C-1. Linear Pair Conjecture (pg. 120) - If two angles form a linear pair then the two angles are supplementary.

C-2. Vertical Angle Conjecture (pg. 121) Ð'- If two angles are vertical angles then the two angles are congruent.

C-3. Parallel Lines Conjecture (pg. 127) Ð'- If two parallel lines are cut by a transversal, then the corresponding angles are equal.

C-4. Converse of the Parallel Lines Conjecture (pg. 129) Ð'- If two parallel lines are cut by a transversal, then alternate interior angles are equal.

C-5. Perpendicular Bisector Conjecture (pg. 148) Ð'- If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.

C-6. Converse of the Perpendicular Bisector Conjecture (pg. 149) Ð'- If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

C-7. Shortest Distance Conjecture (pg. ?) Ð'- The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.

C-8. Angle Bisector Conjecture (pg. 157) - If a point is on the bisector of an

angle, then it is equidistant from the sides of the angle.

C-9. Angle Bisector Concurrency Conjecture (pg. 176) Ð'- The three angle bisectors of a triangle are concurrent.

C-10. Perpendicular Bisector Concurrency Conjecture (pg. 177) - The three

perpendicular bisectors of a triangle are concurrent.

C-11. Altitude Concurrency Conjecture (pg. 177) - The three altitudes (or the

lines containing the altitudes) of a triangle are concurrent.

C-12. Circumcenter Conjecture (pg. 177) - The circumcenter of a triangle is the

point of concurrency of the three perpendicular bisectors.

C-13. Incenter Conjecture (pg. 178) Ð'- The incenter of a triangle is the point of

concurrency of the three angle bisectors.

C-14. Median Concurrency Conjecture (pg. 183) - The three medians of a triangle

are concurrent.

C-15. Centroid Conjecture (pg. 184) - The centroid of a triangle devides each

median into two parts so that the distance from the centroid to the vertex is

equal to the distance from the centroid to the midpoint on the opposite side.

C-16. Center of Gravity Conjecture (pg. 185) - The centroid of a triangle is the center of gravity of the triangular region.

C-17. Triangle Sum Conjecture ( Pg. 199)