Cheat Sheet.notebook
November 28, 2011
Proving Triangles Congruent Cheat Sheet
Steps in writing a proof:
1. Read what is given in the problem
2. Mark the given in your picture
3. Make a statement and reason chart
Statements
Reasons
1.
Rewrite the given
1. Given
2.
2.
.
.
.
.
.
.
n. Rewrite Prove
n. SSS, SAS, ASA, AAS, HA, LA, LH, LL or CPCTC
4. Possible REASONS: Theorem
Postulate
Definition
Algebra Property
NOTE: When you state triangles are congruent write them in corresponding order
When two triangles share a side:
The shared side will be congruent because of ________________
A
Statement
Reason
B
D
C
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Cheat Sheet.notebook
November 28, 2011
When two triangles are sharing an angle:
That shared angle will be congruent because of ______________
B
Statement
Reason
D
F
E
A
C
If a point is the midpoint of a segment, then
­The segment with the midpoint is now divided into two ____________ parts
­The parts are congruent because of ___________
Given: D is the midpoint of BC
A
Statement
Reason
B
D
C
2
Cheat Sheet.notebook
November 28, 2011
In a picture where two lines cross:
The angles opposite each other are _____________
The angles are congruent because of ______________
Statement
Reason
E
A
C
B
D
When you have two perpendicular (⊥) segments:
Perpendicular lines form ________________
Angles are right angles by _____________
State the triangles are right triangles by ________
A
Given: AD ⊥ BC
Statement
Reason
B
D
C
3
Cheat Sheet.notebook
November 28, 2011
When a line/ray bisects an angle:
The angle that it bisects is now cut into __________
Set each new angle congruent to each other the reason is __________________
Given: AD bisects BAC
Statement
A
Reason
B
C
D
When two segments bisect each other:
Each segment is now cut into ____________
Set each part of the segment congruent to the other part the reason is ________________________
Given: AD and BE bisect each other
Statement
Reason
E
A
C
B
D
4
Cheat Sheet.notebook
November 28, 2011
If you have an angle outside the triangle you are trying to prove congruent and it is a supplement to an angle in your triangle:
Set the two angles inside the triangle congruent to each other. Reason _____________________
Given: CDF and EDF are congruent
Statement
Reason
If you have an angle outside the triangle you are trying to prove congruent and it is a complement to an angle in your triangle:
Set the two angles inside the triangle congruent to each other. Reason _________________________
Given: CF⊥ AD, CF bisects ACD BFA and EFD are congruent
Prove: FBC ≅ FEC Statement
Reason
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Cheat Sheet.notebook
November 28, 2011
If they say Perpendicular Bisector ( ⊥ ) Angles are right angles by _________
State right triangles by ____________
State segments congruent by ________
A
Given: AD BC
Statement
Reason
B
D
C
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