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

≅

≅

≅ ≅∠ ≅∠