Name:_________________________________
Special Steps in Proofs
Date:_______ Period:_____
Ms. Anderle
Special Steps in Proofs
Perpendicular: 3 steps
1. AB  CD
2. <CBA and <DBA are right angles
3.  CBA  DBA
A
1. Given
2. Perpendicular lines form right angles
3. All right angles are congruent
Bisectors: 2 steps
(a bisector can divide an angle
or a line segment. Look carefully)
1. AB bisects <CBD
2.  CBA  DBA
A
1. Given
2. An angle bisector divides an angle
into two congruent angles.
Midpoint: 2 steps
*A segment bisectors and a midpoint BOTH
divide a segment into two congruent segments --but don’t say one name instead of the other!
1. AD is the midpoint of BC
2. BD  DC
S
1. Given
2. A midpoint divides a segment into
two congruent segments.
Overlapping Triangles: 4 steps to get the
overlapping sides.
The given sides are too short.
1.
2.
3.
4.
AB  CD
BC  BC
AB  BC  CD  BC
AB  CD
S
1. Given
2. Reflexive Property
3. Addition Postulate
4. Substitution
The given sides are too long: 4 steps
1.
2.
3.
4.
AC  DB
BC  BC
AC  BC  DB  BC
AB  CD
S
Remember:
Too Short:
Given, reflexive, addition substitution
Too Long:
Given, reflexive, subtraction, substitution
1. Given
2. Reflexive Property
3. Subtraction Postulate
4. Substitution
For supper, we need:
1) Milk
2) Bread
3) Eggs
Supplementary Angles:
3 steps
(look for an extended
straight line)
1.  1  2
2. <1 & <3 are supplementary
<2 & <4 are supplementary
3.  3  4
S
1. Given
2. Angles from a linear pair are
supplementary
3. Supplements of  <’s are 
Remember:
If you run out of givens, you have two choices:
Intersecting lines form
congruent vertical angles
Reflexive Property