Geometry
Review Chapter 4
Name ___________________________
Find the measure of the indicated angle.
1.  ACT   NOW.
a)
mT =
b)
mN =
c)
mC =
a) m P 
2. WXYZ  PQRS
b) QR =
c) m X =
3. Given
DEF  LMN .
a) E  L ___________
4. If
mF  5x
and
True or False.
b)
EF  MN __________________ c) FE  NL _________________
mN  2x  12 , find mF =_____________________
State the postulate or theorem you would use to prove each pair of triangles congruent. If the triangles cannot be proved
congruent, write not possible.
5. __________________
6. ________________
7. __________________
8. ________________
9. ________________
10. ___________________
Tell whether the HL Theorem can be applied to prove the triangles are congruent. If not, what is missing?
11.
12.
13. Find the measures of the missing angles.
x  _______
a)
b)
y  _______
x  _____
c).
m
= _______
n = _______
x  _____
d)
y  _____
14. Given: mBCD  20 and
0
a)
y  _____
AD  11
m1=___________
b) AB = _________________
15.
a) If AE || BD, then 1  ______________
Justification: ______________________
b) If B is the midpoint of AC, then AB  ___________
Justification: ________________________________
c) If A  E then
AC  _______________
Justification: _______________________________________
Proofs.
16. Given: RS bisects GRH , G  H
Prove: GS  HS
17. Given :
Prove:
18.
19.
Prove:
20. Solve by substitution.
21. For what values of x and y are the triangles
congruent by HL.
Geometry Answers-Review Chapter 4
1. a) 52 b) 28 c)100
2. a) 80 b) 3 c) 100
3. a) False b) True c) False
4. 20
5. ASA
6. SAS
7. AAS
8. not possible
9. SSS
10. SAS
11. Yes
12. No, don’t know if right triangle
13.a) x=60, y=30 b) m=60, n=30
c) x=65, y=90
d) x=55, y=62.5
14. a) 40 b) 11
3 , Corresponding Angles Thm.
b) BC , definition of midpoint
c) CE , Isosceles Triangle Thm.
15. a)
16. Proof:
1. RS bisects GRH 1. Given
2. G  H
2. Given
3. 1  2
3. Def. of bisector
4. Reflexive Prop.
RS  RS
GRS  HRS 5. AAS
6. GS  HS
6. CPCTC
4.
5.
17. Proof:
1. AB  QT
1. Given
2. AC  QJ
2. Given
3. A  Q
3. Given
4. BAC  TQJ 4. SAS
5. TJ  BC
18. Proof:
5. CPCTC
1. M is the midpoint of XY 1. Given
2. AX  AY
2. Given
3. AM  AM
3. Reflexive
4. XM  MY
5. AMX  AMY
19. Proof:
HF  HJ
2. FG  JK
1.
4. Def’n. of midpoint
5. SSS
1. Given
2. Given
3. H is midpoint of GK 3. Given
4. GH=HK
4. Def’n. of midpoint
5. FHG  JHK
5. SSS
6. G  K
6. CPCTC
20. (2, 2)
21. x = 3, y = 2