Download Triangle Proof Notes

CCGPS Geometry
1- Similarity, Congruence & Proofs
1.9 – Practice
Name: ________________________________________________ Date: _______________________
Triangle Proofs
Flow Chart Proofs:
A flow chart proof is a concept map that shows the statements and reasons needed for
a proof in a structure that helps to indicate the logical order. We typically will be looking
for statements that provide sides or angles needed in the congruence postulates.
Statements, written in the logical order, are placed in the boxes. The reason for each
statement is placed under that box.
Example:
Given: AD  CD, AB  CB
Prove: A  C
Practice #1:
Given: PNQ  LNM , PN  LN , N is the midpoint of QM .
Prove: PQ  LM
Practice #2:
Given: BA  DC , BD bisects AC , AC bisects BD
Prove: ABE  DCE
CCGPS Geometry
1- Similarity, Congruence & Proofs
1.9 – Practice
2 Column Proofs:
A deductive argument that contains statements and reasons organized in two columns.
Problem 1: Given: LM  LO , MN  ON
Statement
1. LM  LO
2. MN  ON
3. LN  LN
4. LMN  LON
Problem 2: Given: QS RT , R  S
Statement
1. QS RT
2. 1  2
3. R  S
4. QT  QT
5. QST  TRQ
Reason
1.
2.
3.
4.
Reason
1.
2.
3.
4.
5.
Problem 3: Given: GI  KI , HI  JI
1.
2.
3.
4.
Statement
GI  KI
HI  JI
GIH  KIJ
GIH  KIJ
Problem 4: Given: AC BD, AB CD
Statement
1. AC BD, AB CD
2. 1  4, 2  3
3. AD  AD
4. ADC  DAB
Reason
1.
2.
3.
4.
Reason
1.
2.
3.
4.
Choices for problems #1 – 4 (some will be used more than once):
AAS
ASA
Alternate Interior Angles are 
Right Angle Congruence
Given
Reflexive Property
SAS
SSS
Vertical Angles are 
CCGPS Geometry
1- Similarity, Congruence & Proofs
Problem 5: Given: I  K , IHJ  KJH
Statement
1. I  K
2. IHJ  KJH
3. HJ  HJ
4. HJK  JHI
Problem 6: Given: PQ  QS , QT  QR
Statement
1. PQ  QS
2. QT  QR
3. PQT  RQS
4. PQT  SQR
1.9 – Practice
Reason
1.
2.
3.
4.
Reason
1.
2.
3.
4.
Problem 7: Given: UWV and UWX are right angles.
Statement
Reason
1.
1.
2.
2. Right Angle Congruence
3.
3. V  X
4.
4. Reflexive Property
5. UWV  UWX 5.
Problem 8: Given: Y  C , YA  CA
Statement
1. Y  C
2.
3.
4. YZA  CBA
Problem 9: Given: KOL  NML, LO  LM
Statement
1.
2.
3.
4. KLO  NLM
5. K  N
Reason
1.
2.
3. Vertical Angles
4.
Reason
1.
2.
3.
4.
5.