Download The Tool Box (through Ch.3)

Proof Tool Box
- SEGMENTS Midpoint:
A point bisects a segment into two congruent segments
iff it is the midpoint.
Angle Addition Postulate:
mABD  mDBC  mABC
Segment Addition Postulate:
AB + BC = AC iff B is between A and C.
Angle Bisector:
A ray that divides an angle into two congruent angles.
Segment Bisector:
A segment, ray, line, or plane that intersects a plane at
its midpoint.
Congruent Angles:
Two angles are congruent iff their measures are
equal.
- ALGEBRA PROPERTIES -
Complimentary Angles:
Two angles are complimentary iff the sum of their
measures is 90 degrees.
Addition Property:
If a = b, then a + c = b + c
Subtraction Property:
If a = b, then a – c = b – c
Multiplication Property:
If a = b, then ac = bc
Division Property:
If a = b, then a/c = b/c
Reflexive Propery:
a=a
Symmetric Property:
If a = b, then b = a
- ANGLES -
Congruent Compliments Theorem:
If two angles are complimentary to the same angle,
then they are congruent.
Ex) If 1 and 2 are complementary and
2 and 3 are complementary,
then 1  3 .
Supplementary Angles:
Two angles are supplementary iff the sum of their
measures is 180 degrees.
Congruent Supplements Theorem:
If two angles are supplementary to the same angle,
then they are congruent.
Acute Angle: An angle is acute iff its measure is less than 90 degrees.
Right Angle: An angle is a right angle iff its measure is 90 degrees.
Transitive Property:
If a = b and b = c, then a = c.
Obtuse Angle: An angle is obtuse iff its measure is greater than 90 degrees.
Straight Angle: An angle is straight iff its measure is 180 degrees.
Substitution Property:
If a = b, then you can substitute a in for b.
- INTERSECTING LINES Vertical Angles Theorem:
Vertical angles are congruent.
Linear Pair Postulate:
If two angles form a linear pair, then they are
supplementary.
MORE ON THE NEXT SIDE…
Proof Tool Box
- POINTS / LINES / PLANES  Through any two points there exists exactly one line.
 A line contains at least 2 points
 If two lines intersect, then their intersection is exactly one point
 Through any 3 non-collinear points, there exists 1 plane
 A plane contains at least 3 non-collinear points
 If 2 points lie on the same line, them lies in the same plane.
 If 2 planes intersect, then their intersection is a line.
- PERPENDICULAR Perpendicular Lines:
Two lines are perpendicular iff they intersect to form a
right angle.
Perpendicular Lines Cut By Transversal
Perpendicular Transversal Thm:
If a transversal is perpendicular to one of the two
parallel lines, then it is perpendicular to the other.
**If 2 lines are perpendicular to the same line, then they
are parallel to each other.
- PARALLEL Parallel Lines:
Two lines are parallel iff they do not intersect and are
coplanar.
Parallel Lines Cut By Transversal
Corresponding Angles Postulate:
If parallel lines are cut by a transversal, then
corresponding angles are congruent.
Alternate Interior Angles Thm:
If parallel lines are cut by a transversal, then alternate
interior angles are congruent.
Consecutive Interior Angles Thm:
If parallel lines are cut by a transversal, then
consecutive interior angles are supplementary.
Alternate Exterior Angles Thm:
If parallel lines are cut by a transversal, then alternate
exterior angles are congruent.
**The converse of each is also true.
**Do not remember these by their name…. remember them by their definition.
**If 2 lines are parallel to the same line, then they are
parallel to each other.
**If 2 lines are perpendicular to the same line, then
they are parallel to each other.