2-COLUMN PROOFS
To complete your proof, first list the parts that are given.
Choose from the following as reasons for your statements.
Reflexive Property Vertical Angles Alternate Interior Angles Def. of bisector
Def. of Perpendicular Def. of Midpoint SAS AAS ASA SSS HL
GIVEN:
AE bisects BD
BD bisects AE
Prove:
ΔABC ≅ ΔEDC
Statements
1
AE bisects BD
2
BC ≅ CD
3
BD bisects AE
4
AC ≅ CE
5
∠ACB ≅ ∠ECD
6
ΔABC ≅ ΔEDC
GIVEN:
AD ≅ BC
∠ACD and ∠CAB
are right angles
Reasons
Prove:
ΔABC ≅ ΔCDA
Statements
1
2
AC ≅ AC
3 ∠ACD and ∠CAB
are rt ∠s
4
ΔABC ≅ ΔCDA
GIVEN:
∠NIO ≅ ∠NGD
NO ≅ ND
GIVEN:
RS ≅ AT
RS ∥ TA
Prove:
ΔINO ≅ ΔGND
Prove:
ΔART ≅ ΔSTR
Statements
1
2
3
4
5
Reasons
Given
Given
∠N ≅ ∠N
ΔINO ≅ ΔGND
GIVEN:
MA ≅ HV
MV ≅ HA
1
2
3
4
Given
Reflexive
ΔART ≅ ΔSTR
Prove:
ΔHOS ≅ ΔROS
Reasons
given
𝑉𝐴 ≅ AV
ΔVAM ≅ ΔAVH
Reasons
GIVEN:
HO ≅ OR
HS ≅ 𝑅𝑆
Prove:
ΔVAM ≅ ΔAVH
Statements
MV ≅ HA
1
2
3
4
5
Statements
RS ∥ TA
∠TRS ≅ ∠ATR
Reasons
1
2
3
4
Statements
HO ≅ OR
Reasons
given
ΔHOS ≅ ΔROS
2-COLUMN PROOFS
To complete your proof, first list the parts that are given.
Choose from the following as reasons for your statements.
Reflexive Property Vertical Angles Alternate Interior Angles Def. of bisector
Def. of Perpendicular Def. of Midpoint SAS AAS ASA SSS HL
GIVEN:
AE ∥ 𝑅𝐷
AE ≅ RD
GIVEN:
AE bisects BD
AB ∥ 𝐷𝐸
Prove:
ΔRED ≅ ΔADE
Prove:
ΔABC ≅ ΔEDC
Statements
1
2
3
4
5
6
1
2
3
4
5
Statements
AE ∥ 𝑅𝐷
∠𝐴𝐸𝐷 ≅ ∠𝑅𝐷𝐸
Reasons
Given
reflexive
ΔRED ≅ ΔADE
GIVEN:
AC ≅ ED
∠A ≅ ∠D
GIVEN:
HR ⊥ TA
HT ≅ AR
𝐸 is the midpoint of 𝐴𝑇
Prove:
ΔHET ≅ ΔREA
Prove:
ΔDEB ≅ ΔACB
Statements
1
2
3
4
Statements
Reasons
Given
Given
Reflexive
AAS
GIVEN:
𝐵𝐼 ∥ 𝑅𝐷
BR bisects ID
Prove:
ΔBIS ≅ ΔRDS
Statements
1
𝐵𝐼 ∥ 𝑅𝐷
2
∠𝐵 ≅ ∠𝑅
3
4
𝐼𝑆 ≅ 𝐷𝑆
5
∠𝐵𝑆𝐼 ≅ ∠𝑅𝑆𝐷
6
Reasons
Reasons
1
2
3
4
5
6
Given:
𝐴𝐵 ∥ 𝐶𝐷
𝐴𝐵 ≅ 𝐷𝐶
Prove:
ΔAEB ≅ ΔDEC
Reasons
Statements
1
2
3
4
5
Reasons
Given
∠𝐸𝐴𝐵 ≅ ∠𝐸𝐷𝐶
∠𝐴𝐵𝐸 ≅ ∠𝐷𝐶𝐸
Given
ΔAEB ≅ ΔDEC