Download Triangle Proofs Reference Sheet

Triangle Proofs Reference Sheet
Proving Sides are 
Possible Reason to Use …
- Reflexive
If you have …
- shared side 
- sides of a midpoint

- definition of midpoint
- sides of a  (perpendicular) bisector
- sides of a bisector 

-sides connecting vertex and end of
 bisector
- sides opposite

angles 
- sides that are part of a

whole
MISC:
1  2; 2  3; 1  3
A  B; C  B; B  30
so A  30 & C  30
If you have …
 & want angles 
- s opposite  legs of a 
-
- any point on a  bisector is
equidistant from the endpoints
- prove 2 s then side in sequence
are 
- if s of  are  then sides
opposite are 
- prove a side b/w 2 s are
- parts of a
are 
MISC:
Transitive

whole with

pieces
Proving Angles are 
Possible Reason to Use …
s being bisected 
s on parallel lines 
s of isosceles  are 
- if sides of  are  then s opp are 
- base
- definition of bisect
- if lines are || then alt. int. s are 
OR …then corresponding s are 
- vertical
- complementary

- prove an  b/w 2 sides are
- definition of bisect
- SAS (side, angle, side)
- AAS (angle, angle, side)

- ASA (angle, side, angle)
- if right s prove a leg and the
hypotenuse are 
- HL (hypotenuse, leg)
Substitution
- isosceles
-
From www.mrs--nelson.webs.com
Proving s are 
First …
THEN Possible Reason to Use …
- prove three sides are 
- SSS (side, side, side)
s shared
s are 
- if s are comp to  s then they are
also  (works for supp also)
s are supp to  s then they are also
- linear pair shared
- if
-  s are 90˚ (or right angles)
- right s 
- 2 s  2 s
- divided  with  s
- definition of 
- all right s are 
- Third Angles Theorem
- parts of a  whole with

 pieces are 
After Proving s are
First …
- prove 1 or 2 sets of s are
-then


then Proving parts are 
THEN Possible Reason to Use …
- CPCTC
Corresponding
Parts of
Congruent
Triangles are
Congruent