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Transcript
Geometry Toolbox (Initial - Big Ideas)
Definitions (Reversible)
Congruent
If two segments or angles are congruent, then they have the same measure.
Right Angle
If an angle is a right angle, then it has a measure of 900.
Straight Angle
If an angle is a straight angle, then it has a measure of 1800.
Midpoint
If a point is a midpoint, then it divides a segment into 2 congruent segments.
Segment Bisector
If a point, segment, ray, or line bisects a segment, then it divides a segment into 2 congruent segments.
Angle Bisector
If a segment, ray, or line bisects an angle, then it divides an angle into 2 congruent angles.
Complementary
If two angles are complementary, then they add to form a right angle or 900.
Supplementary
If two angles are supplementary, then they add to form a straight angle or 1800.
Perpendicular
If two segments, rays, or lines are perpendicular, then they intersect to form right angles.
Theorems and Postulates (Not reversible)
Contrapositive
Right Angle Congruence
If a conditional statement is true, its contrapositive is true. (If p  q is true, then
q  p is true)
If two angles are right angles, then they are congruent.
Straight Angle Congruence If two angles are straight angles, then they are congruent.
Vertical Angles Congruence If two angles are vertical angles, then they are congruent.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Congruent Complements
If two angles are complementary to the same angle (or congruent angles), then they are congruent.
Congruent Supplements
If two angles are supplementary to the same angle (or congruent angles), then they are congruent.
Corresponding Angles
If lines are parallel, then corresponding angles are congruent.
Alternate Interior Angles
If the lines are parallel, then alternate interior angles are congruent.
Alternate Exterior Angles
If the lines are parallel, then alternate exterior angles are congruent.
Same-side Interior Angles
If the lines are parallel, then same-side interior angles are supplementary.
Same-side Exterior Angles
If the lines are parallel, then same-side exterior angles are supplementary, then.
Converse Corresponding Angles
If corresponding angles are congruent, then the lines are parallel.
Converse Alternate Interior Angles
If alternate interior angles are congruent, then the lines are parallel.
Converse Alternate Exterior Angles
If alternate exterior angles are congruent, then the lines are parallel.
Converse Same-side Interior Angles
If same-side interior angles are supplementary, then the lines are parallel.
Converse Same-side Exterior Angles
If same-side exterior angles are supplementary, then the lines are parallel.
Miscellaneous

Addition = Adding two or more angle measures or segment lengths.

Subtraction = Subtracting two or more angle measures or segment lengths.

Transitive Property = Only congruent statements, linked together.

Substitution Property = Replacing a segment or angle using congruency.

Symmetric Property = If A = B, then B = A.

Reflexive Property = A segment or angle is congruent to itself.

Distribution Property = When multiplying into parenthesis, then you multiply each term by the number in front.