Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
Period:
PROOF 1
B
Given:
AC is the angle bisector of BAD
A
AB  AD
C
Prove:
ABC  ADC
D
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Page 1 of 7
Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
Period:
PROOF 1 statements and reasons
̅̅̅̅
𝐴𝐶 is the angle bisector of BAD
Reflexive Property
Side Angle Side (SAS)
AB  AD
AC  AC
ABC  ADC
BAC  DAC
Given
Given
Definition of angle bisector
PROOF 2 statements and reasons
*You will not use all of these for a complete proof
ACB  DEB
Definition of vertical angles
BCA  BED
CBA  EBD
Alternate Interior Angles
Given
∠𝐵𝐷𝐸 ≅ ∠𝐵𝐴𝐶
CB  EB
Alternate Interior Angles
Angle Angle Side (AAS)
BAC  DAC
Angle Side Angle (ASA)
Given
l m
Page 2 of 7
Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
Period:
PROOF 2
t
A
l
C
l m
CB  EB
B
E
Statement
Given:
D
m
Prove:
ACB  DEB
Reason
Page 3 of 7
Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
Period:
PROOF 3
B
A
Statement
D
Given:
BD is the  bisector of AC
AB  CB
C
Prove:
ADB  CDB
Reason
Page 4 of 7
Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
PROOF 3 statements and reasons
Period:
*You will not use all of these for a complete proof
AB  CB
AD  CD
Definition of perpendicular bisector
ADB and CDB are right triangles
Given
BDA and BDC are right angles
Definition of perpendicular bisector
Given
BD is the  bisector of AC
Side Angle Side (SAS)
Hypotenuse Leg (HL)
BD  BD
Reflexive Property
Side Side Side (SSS)
Definition of right triangle
∠𝐵𝐷𝐴 ≅ ∠𝐵𝐷𝐶
All right angles are congruent
mBDA  90
mBDC  90
Page 5 of 7
Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
Period:
Paragraph Proofs – Use the example provided for Proof 1 as a model to convert Proof 2 and Proof 3 into
paragraph proofs.
PROOF 1
̅̅̅̅ is the angle bisector of ∠𝐵𝐴𝐷 and ̅̅̅̅
̅̅̅̅ is the angle bisector
It is given that 𝐴𝐶
𝐴𝐵 ≅ ̅̅̅̅
𝐴𝐷. Since 𝐴𝐶
of ∠𝐵𝐴𝐷, it is known that ∠𝐵𝐴𝐶 ≅ ∠𝐷𝐴𝐶 because the angle bisector divides an angle into two
̅̅̅̅ is a side of both triangles, it is congruent to itself by the reflexive
congruent angles. Since 𝐴𝐶
property. Therefore by SAS (side angle side), ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶, because if two sides and the
included angle of one triangle are congruent to the corresponding parts of another triangle, the
triangles are congruent.
PROOF 2
Page 6 of 7
Curriculum 2.0 Geometry: Unit 1-Topic 4, SLT 37
Name:
Prove This
Date:
Period:
PROOF 3
Page 7 of 7