1. C 2. E 3. F4. A 5. B 6. D
14. x = 60° 15. x = 30 16. x = 134
17. x = 47 18. x = 36 21. 50°
22. 130° 23. 50° 24. 130°
25. 40° 26. 30°
27. x = 45°; 45°, 45°, 90 32. x = 43°, y = 32°
4.1 HW pg. 221 #1-6, 14-18, 21-27, 32, 33, 354.2a HW pg. 229 #15, 16, 19, 20
33. x = 118°, y = 96°
35. x = 26°, y = 64°
15. x = 20 16. x = 11 19. x = 3°, y = 1°
20. x = 5, y = 2
4.1 HW pg. 221 #1-6, 14-18, 21-27, 32, 33, 354.2a HW pg. 229 #15, 16, 19, 20
3.
BCA EFD
5. 124° 6. 33° 7. 8
8. 9. ZYX 10. NML
11. XYZ ZWX, all parts are congruent
12. Not congruent 21. B
4.2b HW pg. 228 #3, 5-12, 214.3 HW pg. 237 #1-7, 16, 17, 24, 26
A D
B E
C F
∠ ≅∠∠ ≅∠∠ ≅∠
AB DE
BC EF
AC DF
≅
≅
≅
NL
1. Angles 2. Neither 3. Sides
4. Neither 5. No, RST PQT 6. Yes, SSS
7. Yes, SSS 16. B 17. B
21.
4.2b HW pg. 228 #3, 5-12, 214.3 HW pg. 237 #1-7, 16, 17, 24, 26
Given
Given
Reflexive
GHJ SSS
GH JK
HJ KG
GJ GJ
JKG
≅
≅
≅ ≅
26.
4.2b HW pg. 228 #3, 5-12, 214.3 HW pg. 237 #1-7, 16, 17, 24, 26
Given
Given
is the midpt. of Given
Def. of Midpt
SSS
AE CE
AB CD
E BD
BE ED
EAB ECD
≅
≅
≅ ≅
1. Included 3. ∠XYW 5. ∠ZWY
7. ∠XYZ 8. Not enough 9. Enough
10. Enough 11. Not enough 13. Enough
14. Not enough 20. Not enough 21. SAS
25.
26.
27.
4.4 HW pg. 243 #1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38
AC DF≅
AB DE≅
BC EF≅
Mark Pictures!
34.
4.4 HW pg. 243 #1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38
35.
4.4 HW pg. 243 #1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38
bisects Given
Def. of angle bisector
Given
Reflexive
SAS
PQ SPT
SPQ TPQ
SP TP
PQ PQ
SPQ TPQ
∠∠ ≅∠
≅
≅ ≅
37.
4.4 HW pg. 243 #1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38
Given
Reflexive
& are right triangles Given
JM LM
KM KM
JKM LKM
JKM LKM
≅
≅ ≅ HL
38.
4.4 HW pg. 243 #1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38
is the midpoint of Given
Def. of midpt
Reflexive
Given
SAS
D AC
AD DC
BD BD
ADB CDB
ABD CBD
≅
≅∠ ≅∠ ≅
3. Yes, AAS 4. No 5. Yes, ASA
6. No, AAA 7. B 8. ∠F ∠L
9. ∠F ∠L 10. 14. Yes, SAS
15. No, AAA 16. Yes, AAS 17. Yes, SSS
18. No
4.5 HW pg. 252 #3-10, 14-18WS
GH MN≅
4.5 HW pg. 252 #3-10, 14-18WS
GivenDef. of angle bisector
GivenReflexive
AAS
1.
Given
Given
Vertical Angles
AAS
BE BC
A D
ABE DBC
ABE DBC
≅∠ ≅∠∠ ≅∠ ≅
2.
4.5 HW pg. 252 #3-10, 14-18WS
Given
Alternate Interior Angles
Given
Reflexive
ASA
AB DC
ABD CDB
ADB CBD
BD BD
ABD CDB
∠ ≅∠∠ ≅∠
≅ ≅
3.
4.5 HW pg. 252 #3-10, 14-18WS
Given
Given
Reflexive
AAS
XYW ZWY
WXY YZW
WY WY
ZWY XYW
∠ ≅∠∠ ≅∠
≅ ≅
4.
4.5 HW pg. 252 #3-10, 14-18WS
Given
Given
Vertical Angles
AAS
D C
AB EB
ABD EBC
DBA CBE
∠ ≅∠
≅∠ ≅∠ ≅
5.
4.5 HW pg. 252 #3-10, 14-18WS
4.6 HW pg. 259 #1-5odd, 6WS
1. Congruent
3. ABC DBC by SSS
5. JKM LKM by HL
6. CAD BDA by AAS
1.
4.6 HW pg. 259 #1-5odd, 6WS
Given
Def. of midpoint
Def. of midpoint
SAS
CPCTC
Vertical angles
2.
4.6 HW pg. 259 #1-5odd, 6WS
Given
Given
Reflexive
SSS
CPCTC
VW XY
WX YV
VX VX
YVX WXV
Y W
≅
≅
≅ ≅∠ ≅∠
3.
4.6 HW pg. 259 #1-5odd, 6WS
bisects Given
Def. of segment bisector
Given
Vertical Angles
AAS
R QT
QR RT
U S
QRU TRS
QUR TSR
ST U
≅∠ ≅∠∠ ≅∠ ≅
≅ CPCTCQ
4.
4.6 HW pg. 259 #1-5odd, 6WS
Given
& are right angles Def. of lines
& are right triangles Def. of right angle
DB AC
ABD CBD
ABD CBD
AD CD
⊥∠ ∠ ⊥
≅ Given
Reflexive HL
BD BDABD CBD
AB CB
≅ ≅
≅ CPCTC
5.
4.6 HW pg. 259 #1-5odd, 6WS
is the midpoint of Given
Def. of midpoint
Given
Vertical Angles
B DC
DB BC
D C
ABD EBC
AB
≅∠ ≅∠∠ ≅∠ ASA
CPCTCD EBC
A E≅
∠ ≅∠
4.7 HW pg. 267 #3-13, 15-17, 19
3. ∠A ∠D by the Base Angle Theorem
4. ∠A ∠BEA by the Base Angle Theorem
5. by the Base Angle Theorem Converse
6.
7. 12 8. 16 9. 60°
10. Base Angles: 37°, vertex angle: 106°
11. x = 20 12. x = 6 13. x = 8
CD CE≅
EB EC≅
4.7 HW pg. 267 #3-13, 15-17, 19
15. x = 39°, y = 39°
16. x = 48°, y = 70°
17. x = 45°, y = 5°
19. B
Marking Triangles Worksheet
1.
______ _______
by ____________
2.
______ _______
by ____________
ABC ECD
SAS
ACB ECD
AAS
3.
______ _______
by ____________
4.
______ _______
by ____________
ABC ECD
AAS
ABC EDC
AAS
Marking Triangles Worksheet
Marking Triangles Worksheet
5.
______ _______
by ____________
6.
______ _______
by ____________
ABC ADC
SAS
ABC ADC
SSS
Marking Triangles Worksheet
7.
______ _______
by ____________
8.
______ _______
by ____________
BAC DAC
AAS
ABC ADC
ASA
Marking Triangles Worksheet
9.
______ _______
by ____________
10.
______ _______
by ____________
ABD CBD
HL
ADB CDB
SAS
Marking Triangles Worksheet
11.
______ _______
by ____________
12.
______ _______
by ____________
ADB CDB
SAS
ADB CDB
SSS
Ch 4 Review pg. 282-285 #1-5odd, 6-13, 15-20, 24, 26 pg. 286 #1-6
1. equiangular
3. Isosceles: 2 congruent sides. Scalene: No congruent sides
5.
6. x = 45°, Exterior angle = 65° 7. x = 15°, Exterior angle = 120°
8. x = 9°, Exterior angle = 90° 9. 60°
10. 15m 11. 60° 12. 50° 13. x = 18
Ch 4 Review pg. 282-285 #1-5odd, 6-13, 15-20, 24, 26 pg. 286 #1-6
15. True, SSS 16. not true, BD CA
17. True, SAS 18. True, HL
19. ∠J ∠F 20. ∠G ∠D
24. x = 65° 26. x = 1
1. Equilateral, Acute 2. Right, scalene
3. Isosceles, Obtuse 4. x = 70°
5. x = 30 6. x = 75°
Proof Review Worksheet
1.
C is the midpoint of & Given
Def. of midpoint
Def. of midpoint
AE BD
AC CE
BC CD
ACB ECD
≅
≅∠ ≅∠ Vertical Angles
SASABC EDC ≅
Proof Review Worksheet
2.
Given
Alternate Interior Angles
Given
Vertical Angles
AAS
AB DE
B E
AB DE
ACB DCE
ABC ECD
∠ ≅∠
≅∠ ≅∠ ≅
Proof Review Worksheet
3.
Given
& are right angles Def. of lines
& are right triangles Def. of right triangles
BD AC
ADB CDB
ADB CDB
AB CB
⊥∠ ∠ ⊥
≅ Given
Reflexive HL
BD BDABD CBD≅
≅
Proof Review Worksheet
4.
bisects Given
Def. of angle bisector
Given
Reflexive
SAS
AC BAD
BAC DAC
AB AD
AC AC
BCA DCA
B
∠∠ ≅∠
≅
≅ ≅∠ CPCTCCA DCA≅∠
Proof Review Worksheet
5.
C is the midpoint of Given
Def. of midpoint
Given
Vertical Angl
BD
BC CD
B D
ACB ECD
≅∠ ≅∠∠ ≅∠ es
ASA
CPCTC
ACB ECD
AB ED
≅
≅
Proof Review Worksheet
6.
Given
Given
Reflexive
SSS
CPCTC
AB AD
BC DC
AC AC
ABC ADC
B D
≅
≅
≅ ≅∠ ≅∠