Download Ch. 5 Review Key

Geometry
REVIEW: Chapter 5
Name _____________________________________
For Questions 1-4, refer to the figure.
1. Name a median. Medians are drawn from a vertex to the MIDDLE of a side (cutting the side in ½)
A 𝑅𝑊
B ⃡𝑆𝑉
C 𝑄𝑇
D 𝑅𝑈
2. Name an angle bisector. Angle bisectors cut angles in ½
A ̅̅̅̅̅
𝑅𝑊
B ⃡𝑆𝑉
C ̅̅̅̅
𝑄𝑇
D 𝑅𝑈
3. Name a perpendicular bisector. Perpendicular bisectors do not have to go through a vertex, but MUST be  at the midpoint
⃡
̅̅̅̅̅
A 𝑅𝑊
B 𝑆𝑉
C ̅̅̅̅
𝑄𝑇
D 𝑅𝑈
4. Name an altitude. Altitudes are drawn from a vertex to the opposite side, making a RIGHT ANGLE
̅̅̅̅̅
̅̅̅̅
A 𝑅𝑊
B 𝑅𝑃
C ̅̅̅̅
𝑄𝑇
D 𝑅𝑈
For Questions 5-7, refer to the figure to determine which is a true statement for the given information.
5. ̅̅̅̅
𝐹𝐺 is an altitude. Altitudes form right angles
A ∠ DGF is a right angle.
B DF = EF
C DG = GE
D ∠ DFG ≅ ∠ EFG
6. ̅̅̅̅
𝐹𝐺 is a median. Medians are drawn from a vertex to the MIDDLE of a side (cutting the side in ½)
A ∠ DGF is a right angle.
B DF = EF
C DG = GE
D ∠ DFG ≅ ∠ EFG
7. ̅̅̅̅
𝐹𝐺 is an angle bisector. Angle bisectors cut angles in ½
A ∠ DGF is a right angle.
B DF = EF
C DG = GE
D ∠ DFG ≅ ∠ EFG
8. Name the longest side of △ABC.
BC (it is across from the largest angle)
9. Name the angle with the greatest measure in △GHI.
I (it is across from the biggest side)
10. Hannah, Brandon, and Angel are friends that live close to one another. Which two friends have the shortest distance between
them? Angel and Brandon live the closest.
(Since 3 s of a  are given, their sum is 180. Set up and solve for x:
13x + 21 + 4x + 28 + 3x =11 = 180. (x = 6).
Angel
Plug x = 6 back into each angle; Hannah = 29, Angel = 99, Brandon =
52. The smallest side will be across from the smallest angle.)
(13x + 21)
(3x + 11)
Hannah
(4x + 28)
Brandon
11. Which of the following sets of numbers can be the lengths of the sides of a triangle? Sum of 2 smallest sides > 3rd side
A 12, 9, 2
B 11, 12, 23
C 2, 3, 4
D √3,√5,√18
12. Write an inequality to describe the possible values of x.
2 < x < 16
(If x is the biggest: 7 + 9 > x, but if x is the smallest: x +7 > 9)
Also can be written separately: x > 2 and x < 16
13. Which of the following sets of numbers can be the lengths of the sides of a triangle? Sum of 2 smallest sides > 3rd side
A 5, 5, 10
B √39, √8 , √5
C 2.5, 3.4, 4.6
D 1, 2, 4
14. Write an inequality
relating m∠1 to m∠2.
m1 < m2
16. Write an inequality about the length of 𝐺𝐻.
15. Write an inequality
relating AB to DE.
AB < DE
17. The  bisectors of ∆XYZ meet at point P.
Find PX. PX = 12
(Since  bisectors meet at a circumcenter, and
circumcenter to corners are =
GH > 7
18. The  bisectors of ∆XYZ meet at point P.
Find PM. PM = 6
(Since  bisectors meet at the incenter, and
incenter to sides are =
X
X
__
__
__
F
__
__
13
B
9
|| |
Y
__
P
12
D
M
N
P
8
|| |
10
Z
Z
6
Y
O
19. L is the centroid of ∆MNO, NP = 12, ML = 10, and NL = 6.
a. PO = ___12____ (centroids are the intersection of medians, and medians intersect sides of a triangleMat the midpoint)
b. MP = __15_____(LP = 5 because it is ½ of 10 since it is the shorter part of the median. 10 + 5 = 15)
c. LQ = ___3_____ (the shorter part of the median is ½ of the longer part)
10
d. NQ = ___9____ (6 + 3 = 9)
Q
R
e. Find the perimeter of ∆NLP P = 23 (6 + 12 + 5)
L
6
N
20. List the sides from biggest to smallest.
AB, BC, AC
B
21. List the angles from largest to smallest.
mM, mL, mN
L
24º
22
10
A
108º
C
M
13
N
12
P
O
22. a) If two sides of a triangle have lengths 9 and 15, can the third side be of length 6?
NO! (9 + 6 = 15, and 2 sides must have a sum larger than the 3 rd side)
b) Write an inequality that describes the length of the third side.
6 < x < 24
(If x is the biggest: 9 +15 > x, but if x is the smallest: x +9 > 15)
Can also be written separately: x > 6 and x < 24
23. Complete with <, >, or =
a. m1 __=___ m2
b. MS __<___ LS
c. m1 _>____ m2
M
I
2
1 2
__
S
99
1
__
6
7
8
T 95
I
6
L
24. Use an inequality to describe the value of x as determined by the Hinge Theorem and its converse.
a) x > 14
b) x > 9 (Set up and solve: 3x + 3 > 2x + 12)
6
3x + 3
x
47°
81
78
8
6
8
74
14
2x + 12
̅̅̅̅ is an altitude of △GHI with point J on ̅̅̅
25. 𝐻𝐽
𝐺𝐼 .If m∠ GJH = (5x + 60), GH = 3x + 5, HI = 8x – 3, JI = 3x – 3, and GJ = x + 6, find
the perimeter of △GHI. Solve 5x+60=90. X =6, substitute x=6 into algebra expressions for the side lengths. GH=23, HI=45, JI=15,
GJ=12. Perimeter of ∆𝐺𝐻𝐼 is 95 units.
H
8x – 3
3x + 5
G x +6
J
3x – 3
I
26. Name the construction in the figure.
Altitude