Geometry Conjectures
Geometry Conjectures
Chapter 2
C1- Linear Pair Conjecture - If two angles form a linear pair, then the measures of the angles add up to 180°.
C2- Vertical Angles Conjecture - If two angles are vertical angles, then they are congruent (have equal measures).
C3a- Corresponding Angles Conjecture- If two parallel lines are cut by a transversal, then corresponding angles are congruent.
C3b- Alternate Interior Angles Conjecture- If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
C3c- Alternate Exterior Angles Conjecture- If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
C3- 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.
C4- 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.
Chapter 3
C5- Perpendicular Bisector Conjecture - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.
C6- 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.
C7- Shortest Distance Conjecture - The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.
C8- Angle Bisector Conjecture - If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
C9- Angle Bisector Concurrency Conjecture - The three angle bisectors of a triangle are concurrent (meet at a point).
C10- Perpendicular Bisector Concurrency Conjecture - The three perpendicular bisectors of a triangle are concurrent.
C11- Altitude Concurrency Conjecture
Chapter 2
C1- Linear Pair Conjecture - If two angles form a linear pair, then the measures of the angles add up to 180°.
C2- Vertical Angles Conjecture - If two angles are vertical angles, then they are congruent (have equal measures).
C3a- Corresponding Angles Conjecture- If two parallel lines are cut by a transversal, then corresponding angles are congruent.
C3b- Alternate Interior Angles Conjecture- If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
C3c- Alternate Exterior Angles Conjecture- If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
C3- 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.
C4- 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.
Chapter 3
C5- Perpendicular Bisector Conjecture - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.
C6- 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.
C7- Shortest Distance Conjecture - The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.
C8- Angle Bisector Conjecture - If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
C9- Angle Bisector Concurrency Conjecture - The three angle bisectors of a triangle are concurrent (meet at a point).
C10- Perpendicular Bisector Concurrency Conjecture - The three perpendicular bisectors of a triangle are concurrent.
C11- Altitude Concurrency Conjecture