3.2 Answers - #2, 4-6, 9-13, 15-17, 23
2. a. SAS
b. None
c. None
d. ASA
4.
Statement
1.
2. EF ≅ HF
3. ∠3 ≅ ∠4
4. EFJ ≅HFG
5.
1.
2.
3.
4.
5.
6.
7.
Reason
1.
2.
3.
4.
Given
Given
Vertical angles are congruent
ASA [ 1, 2, 3]
Statement
RO ⊥ MP
∠MOR is a rt angle
∠POR is a rt angle
∠MOR ≅ ∠POR
MO ≅ OP
RO ≅ RO
MRO ≅PRO
Reason
1.
2.
3.
4.
5.
6.
7.
Given
If 2 segs are perpendicular, then they form a rt angle
Same as #2
If 2 angles are rt angles, then they are congruent
Given
Reflexive Prop
SAS [ 4, 5, 6]
6.
1.
2.
3.
4.
5
6.
Statement

SV bis ∠TSB
∠TSV ≅ ∠BSV

VS bis ∠TVB
∠TVS ≅ ∠BVS
SV ≅ SV
TSV ≅BSV
Reason
1. Given
2. If a ray bis an angle, then it divides the angle into 2 congruent angles
3. Given
4. If a ray bis an angle, then it divides the angle into 2 congruent angles
5. Reflexive Prop
6. ASA [ 2, 4, 5]
9.
Statement
1.
2.
3.
4.
PC ≅ PA
BA ≅ BC
PB ≅ PB
PBA ≅PBC
10.
Reason
1.
2.
3.
4.
Given
Given
Reflexive Property
SSS [ 1, 2, 3]
11.
1.
2.
3.
4.
Statement
∠N is comp to ∠NPO
∠S is comp to ∠SPR
∠NPO ≅ ∠SPR
∠N ≅ ∠S
5. NP ≅ SP
6. NOP ≅SPR
1.
2.
3.
4.
5.
6.
Reason
Given
Given
Given
If angles are comp to congruent angles, then they are congruent
Given
ASA [ 3, 4, 5]
12.
Statement
1. O is the mdpt of AY
2. OA ≅ OY
3. O is the mdpt of XZ
4. OZ ≅ OX
5. ∠YOX ≅ ∠ZOA
6. YOX ≅AOZ
Reason
1.
2.
3.
4.
5.
6.
Given
If a pt is a mdpt, then it divides the seg into 2 congruent segs
Given
If a pt is a mdpt. then it divides the seg into 2 congruent segs
Vertical angles are congruent
SAS [ 3, 4, 5]
13.
Statement
1. EO ≅ KM
2. FO ≅ JM
3. EG ≅ KH
4. F is the mdpt of EG
5. J is the mdpt of KH
6. EF ≅ KJ
7. YOX ≅AOZ
Reason
1.
2.
3.
4.
5.
6.
7.
Given
Given
Given
Given
Given
Division Property
SSS [ 1, 2, 6]
15.
Statement
1.
2.
3.
4.
5.
GH ≅ KJ
GJ ≅ HK
HM ≅ JO
GO ≅ KM
GOJ ≅KMH
Reason
1. Given
2. Addition Property
3. Given
4. Given
5. SSS [ 1, 2, 3]
16.
Statement
1.
2.
3.
4.
5.
6.
∠R ≅ ∠N
RP ≅ NT
RT ≅ NP
TS ≅ OP
SR ≅ NO
NOT ≅RSP
Reason
1. Given
2. Given
3. Given
4. Given
5. Subtraction Property
6. SAS [ 1, 2, 5]
17.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Statement
∠1 ≅ ∠6
∠FBC is a strt angle
∠1 supp to ∠2
∠GEC is a strt angle
∠5 supp to ∠6
∠2 ≅ ∠5
BC ≅ EC
∠3 ≅ ∠4
ABC ≅DEC
Reason
1. Given
2. Assumed from diagram
3. If two angles from a strt angle, then the angles are supp
4. Assumed from diagram
5. If two angles from a strt angle, then the angles are supp
6. If two angles are supp to congruent angles, then they are congruent
7. Given
8. Vertical angles are congruent
9. ASA [ 1, 2, 5]
23.
Statement
1. S and T tri RV
2. RS ≅ ST ≅ TV
3. ∠R ≅ ∠V
4. ∠BST ≅ ∠BTS
5. ∠RST is a strt angle
6. ∠BST supp to ∠BTS
7. ∠STV is a strt angle
8. ∠BTS supp to ∠BTV
9. ∠BSR ≅ ∠BTV
10. BRS ≅BVT
Reason
1. Given
2. If a seg is tri, then it is divided into 3 congruent segs
3. Given
4. Given
5. Assumed from diagram
6. If two angles from a strt angle, then the angles are supp
7. Assumed from diagram
8. If two angles from a strt angle, then the angles are supp
9. If two angles are supp to congruent angles, then they are congruent
10. ASA [ 2, 3, 9]