Download Chapter 4 Supplement Packet

Honors Geometry
Chapter 4 Supplement
Name _____________________________________
1. Tell which triangle is congruent to the given triangle in each diagram.
X
a) W
A
b)
B
E
Y
Z
C
D
a) ∆WXZ  ____________
b) ∆CED  ____________
2. State what additional information is needed in order to have congruent triangles.
a) ASA
D
A
b) SAS
J
O
N
C
K
B
E
D
3. Given: AD  CD
B is the midpoint of AC
Prove: ∆ABD  ∆CBD
A
C
B
D
5 6
4. Given: BC  FE
DC  DE
5  6
Prove: ∆BDG  ∆FDG
C
E
B
F
G
5. Given: NR bisects TRP and TNP
Prove: ∆NTR  ∆NPR
N
T
R
P
L
M
J
6. Given: FH bisects JFG

MGF  KJH
JHF  JFK
JH  FG
Prove: FK  MH
H
M
K
F
G
E
7. Given: AEB  DEC
AE  DE
A  D
Prove: AC  BD
A
8. Given: 5  10
AC  CE
Prove: B  D
B
D
C
E
9 10
B
7
5 6
A
C
8
D
D
9. In isosceles ∆DEF the base is DF. Find the perimeter of the triangle.
x + 12
E
3x + 10
2x + 6
F
10. If the information below is enough to prove ∆DEG  ∆FEG write the abbreviation of a congruence statement that would support
the conclusion. (SSS, SAS, ASA, AAS, or HL) Otherwise put “none”. (There may be more than one answer—list all possibilities)
a) EG  DF
E
b) 1  2; 3  4
3 4
c) 5  6; 3  4
d) EG bisects DEF
e) DE  FE ; G is the midpoint of DF
f) DE  FE ; EG  DF
g) 7  8; 3  4
h) DE  FE ; 5  6
7 5
D
1 2
G
6
8
F
11. Given ∆ABC in which ∆ABC  ∆ACB then what can you conclude about ∆ABC?
12. Given ∆ABC in which ∆ABC  ∆CAB then what can you conclude about ∆ABC?
13. State the angles that are equal.
C
B 2
1
3
4
A
D
14. State the angles that are equal.
G
15
15
F
10
E
15
15. State the sides that are equal.
H
a)
b)
A
45°
B
D
c)
1 2
C
D
F
135°
C
F
E
A
B
4
A
3
D
B
E
For numbers 16 – 33, write A for always, S for sometimes, or N for never.
16. Two triangles are congruent if two angles and a side of one are congruent to two angles and a side of the other.
17. If ΔABC  ΔDEF, then AB  DF .
18. The perimeter of an isosceles triangle with base 10 is 20.
19. In PQRS, if PQ  QR  RS  PS , then 1  2  3  4.
P
S
2
1
3
4
Q
R
20. A right triangle is isosceles.
21. An equilateral triangle is equiangular.
22. The three angles in ∆ABC are congruent to the respective angles in ∆PQR, so the triangles are congruent.
23. An angle is congruent to itself.
24. The base of an isosceles triangle is shorter than the legs.
25. If an angle is obtuse, it is opposite the hypotenuse.
26. A triangle has angles of measures 60°, 60°, 60°.
27. An acute triangle has 3 acute angles.
C
28. A right triangle has 3 right angles.
29. A triangle with 3 congruent sides is congruent to another triangle with 3 congruent sides.
30. If two sides and an angle of one triangle are congruent to two sides and an angle of another triangle, then the triangles are
congruent.
31. If the hypotenuse and leg of one triangle are congruent to the hypotenuse and leg of another triangle, then the triangles are
congruent.
32. Right triangles have two legs and a hypotenuse.
33. Right triangles are congruent.
34. In the diagram, if BC  CD then in order to prove ∆ABC  ∆EDC by HL,
what additional two sides must be congruent?
A
E
B
D
C
35. If AB  BC and C  B, what type of triangle is it?
36. Is the following triangle isosceles, scalene, or equilateral?
3x
(2x + 9)°
4x – 1
(x – 4)°
A
37. Find the measure of angle A.
(2x)°
2x + 4
(x – 5)°
(x + 25)°
D
B
38. The perimeter of ∆BAG is 46. AG = 16, AB = x + 4, BG = 2x + 2
By solving for x, determine whether ∆BAG is scalene, isosceles, or equilateral.
C
A
B
G
A
39. Given: AB  AC
mACD (5x + 30)°
mACB = (3x – 10)°
Find: mB
B
C
40. Given: AM bisects BAC
mBAM = (x + 50)°
mCAM = (3x – 4)°
BM = x – 12
MC = 2x – 41
Find BC.
D
A
B
M
C
41. Two sides of an isosceles triangle with perimeter 220 are in the ratio of 3:4. Find all possible lengths for the base.