Download Proof Cheat Sheet

Proof Cheat Sheet
Name ________________________
Date ____________ Period ______
Postulate/Theorem /Property/Term
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Substitution Property of Equality
Transitive Property of Equality
Transitive Property of Congruence
Reflexive Property of Equality
Reflexive Property of Congruence
Symmetric Property of Equality
Symmetric Property of Congruence
ANGLES
Acute Angle
Obtuse Angle
Right Angle
Straight Angle
Complementary Angles
Supplementary Angles
Congruent Angles
Angle Bisector
Vertical Angle Theorem
Linear Pair Postulate
Angle Addition Postulate
LINES & SEGMENTS
Parallel lines
Perpendicular lines
Congruent Segments
What it states
If 3x – 7 = 14 then 3x = 21
IF 5x + 5 = 10, then 5x = 5
If ½ x = 3 then x = 6
If 5x = 20, then x = 4.
If a = b, then a may be replaced by b in any equation
or expression.
If AB + CD = EF and AB = 10, then 10 + CD = EF by
substitution
If a = b and b=c, then a=c.
If m<1 = m<2 and m<2 = m<3, then m<1 = m<3
If a  b, and b  c, then a  c.
If m<1  m<2 and m<2  m<3, then m<1  m<3
a=a
 AB
If a=b then b = a.
AB
If
Segment Addition Postulate
 CD , then CD 
AB
An angle whose measure is less than 90
An angle whose measure is greater than 90 but less
than 180
An angle whose measure is exactly 90
An angles whose measure is exactly 180
The sum of two angle measures is 90
The sum of two angle measures is 180
Angles that have the same measure
If <1  <2, then m<1 = m<2 (measures are equal)
Divides an angle into two  angles
Vertical angles are 
If two angles form a linear pair, then they are
a) supplementary
b) sum of their measures is 180
If C is in the interior of <AOD, then
m<AOC + m<COD = m<AOD
Coplanar lines that do not intersect
Two lines that intersect to form right angles
Segments that have the same length
If
Midpoint
Segment Bisector
AB
AB
 CD then AB = CD (lengths are equal)
,
Point that divides a segment into two  segments
A segments, ray, or line that intersects a segment at
its midpoint.
If three points A, B, and C are collinear and B is
between A and C, then AB + BC = AC.
TRIANGLES
Acute Triangle
Obtuse Triangle
Right Tringle
Isosceles Triangle
Scalene Triangle
Equilateral Triangle
PARALLEL LINES & ANGLE RELATIONSHIPS
Corresponding Angles Postulate
Corresponding Angles Converse
Alternate Interior Angles Theorem
Alternate Interior Angles Converse
Alternate Exterior Angles Theorem
Alternate Exterior Angles Converse
Same-Side Interior Angles Theorem or
Consecutive Interior Angles Theorem
Same-Side Interior Angles Converse or
Consecutive Interior Angles Converse
A triangle with 3 acute angles
A triangle with one obtuse angle
A triangle with one right angle
A triangle with at least two  sides
A triangle with no  sides
A triangle with three  sides
If two lines are parallel, then corresponding angles
are 
If corresponding angles are , then the lines are
parallel.
If two lines are parallel, then alternate interior
angles are 
If alternate interior angles are , then the lines are
parallel.
If two lines are parallel, then the alternate exterior
angles are 
If alternate exterior angles are , then the lines are
parallel.
If two lines are parallel, then the same-side interior
angles are supplementary.
If same-side interior angles are supplementary, then
the lines are parallel.