Download Chapters 2 * 4 Proofs practice

Chapters 2 – 4 Proofs practice
Chapter 2 Proofs Practice
Commonly used properties, definitions, and postulates
Transitive property
Substitution property
Definition of congruent
Segment addition postulate
Angle addition postulate
Right angles theorem
Definition of supplementary
Definition of complementary
Definition of midpoint
Definition of bisect
Linear pair postulate
Vertical angles theorem
Subtraction property
Provide the missing reasons in the following proofs:
Statements
1.
mLAN  30, m1  15
2.
m1  m2  mLAN
3.
15  m2  30
Reasons
1. Given
2. Angle Add. Postulate
3. Substitution Property
4.
m2  15
4. Subtraction Prop =
5.
m1  m2
5. Transitive Property
6.
AM bisects LAN
6. Definition of bisect
Reflexive property
Transitive property
Substitution property
Definition of congruent
Segment addition postulate
Angle addition postulate
Right angles theorem
Definition of supplementary
Definition of complementary
Definition of midpoint
Definition of bisect
Linear pair postulate
Vertical angles theorem
Subtraction property
Given: 1 and 2 are supplementary, and
1  3
Prove: 3 and 2 are supplementary.
Statements
1.
1& 2 are suppl. ; 1  3
2.
m1  m2  180
3.
m1  m3
4.
m3  m2  180
5.
3 & 2 are supplement ary
Reasons
1. Given
2. Definition of Supplementary
3. Definition of .
4. Substitution Property
5. Definition of supplementary
Reflexive property
Transitive property
Substitution property
Definition of congruent
Segment addition postulate
Angle addition postulate
Right angles theorem
Definition of supplementary
Definition of complementary
Definition of midpoint
Definition of bisect
Linear pair postulate
Vertical angles theorem
Subtraction property
Given: 1 and 2 are complementary
Prove: 3 and 4 are complementary
Given
Definition of Complementary
Vertical Angles Theorem
Definition of Congruent
m3 + m4 = 90°
Substitution Property
3 and 4 are comp.
Def. of complementary
Chapter 3 Proofs Practice
Commonly used properties, definitions, and postulates, and theorems
Alternative interior angles theorem
Alternative exterior angles theorem
Same-side interior angles theorem
Corresponding angle postulate
Alternative interior angles converse
Alternative exterior angles converse
Same-side interior angles converse
Corresponding angle converse
Perpendicular transversal theorem
Given : r s
Justify each statement.
Statements
1.
1 and 2 are supplement ary
Reasons
Linear Pair Theorem
2.
8  4
Alt. Ext. Angles Th.
3.
m2  m3  180
Same-side int s Th.
4.
1  7
Vertical s Th.
5.
2  6
Alt. Int. s Th
6.
8  6
Corr. s Postulate
Alternative interior angles theorem
Alternative exterior angles theorem
Same-side interior angles theorem
Corresponding angle postulate
Alternative interior angles converse
Alternative exterior angles converse
Same-side interior angles converse
Corresponding angle converse
Perpendicular transversal theorem
Given : m8  m5  180
Pr ove : r s
Statements
Reasons
1.
m8  m5  180
1. Given
2.
8  2
2. Vertical Angles Th
3.
5  3
3. Vertical Angles Th
4.
m2  m3  180
4. Substitution Property
5.
r s
5. Same-side int angles converse
Chapter 4 Proofs Practice
Commonly used properties, definitions, and postulates, and theorems
Triangle sum theorem
Exterior angles theorem
Isosceles triangle theorem
Isosceles triangle converse
Definition of congruent triangles (CPCTC)
SSS
SAS
ASA
AAS
HL
Given : B & D are right angles; E is the mp of BD
Pr ove : ABE  CDE
Statements
Reasons
1.
B & D are right s
1. Given
2.
E is the mp of BD
2. Given
3.
B  D
3. All rt s are congruent
4.
BE  ED
4. Def. of Midpoint
5.
BEA  DEC
5. Vertical Angles theorem
6.
ABE  CDE
6. ASA
ASA
Triangle sum theorem
Exterior angles theorem
Isosceles triangle theorem
Isosceles triangle converse
Definition of congruent triangles (CPCTC)
SSS
SAS
ASA
AAS
HL
Given : BD  BE ; BD  DA; BE  EC ; 1  2
Pr ove : DBA  EBC
Statements
1.
2.
BD  BE
BD  DA; BE  EC ; 1  2
Reasons
1. Given
2. Given
3.
D & E are right s
3. Def. of 
4.
BA  BC
4. Isos. Triangle converse
5.
BDA  BEC
5. HL
6.
DBA  EBC
6. CPCTC
1
2
Triangle sum theorem
Exterior angles theorem
Isosceles triangle theorem
Isosceles triangle converse
Definition of congruent triangles (CPCTC)
SSS
SAS
ASA
AAS
HL
Justify each statement using the figure.
Statements
Reasons
2.
m3  m4  180
m4  m2  m6
3.
m3  m2  m6  180
Triangle Sum Theorem
4.
m3  m1 m5
Exterior angles theorem
5.
If DE  FE, then 5  6
1.
Linear Pair Theorem
Ext. angles Theorem
Isosceles Triangle Theorem