Geometry
Chapter 5 EXAM
Basic: 3 points
Proficient: 4 points
Advanced: 6points
Each section is worth 5 points
Matching and fill in the blank
are worth 1 point each
Name ______________________
Date: ______________ Period ______
MUST SHOW ALL WORK FOR FULL CREDIT!
Section 1: Midsegments of Triangles –
B. Find the value of x.
P. Find the value of x.
40
x
40
32
25
A.
25
The height of a building is 150 feet. What is the height of the tree? (image not to scale)
150 ft
Section 2: Bisectors in Triangles
T
B. Using the figure to the right, if we are told QT = 12,
then what is the length of RQ? .
|
|
|
P. Using the figure to the right, find the value of x
(2
2
x+
4)°
30°
S
A. Using the figure to the right, if we are told QR = 6n +3 and TQ = 9n – 15, what is
the measure of QR?
|
Q
R
Section 3: Concurrent Lines, Medians, and Altitudes –MATCHING
Match each picture of a triangle to the word that best describes segment AB.
_____1. Median
a.
b.
_____2. Perpendicular Bisector
_____3. Angle Bisector
c.
d.
e.
_____4. Altitude
_____5. Midsegment
Section 4: Points of Concurrency – MATCHING
Match the definition to the word.
_____ 1. The point of concurrency of the angle bisectors
A. incenter
_____ 2. The point of concurrency of the medians
B. circumcenter
_____3. The point of concurrency of the altitudes
C. centroid
_____ 4. The point of concurrency of the perpendicular bisectors
D. orthocenter
Section 5: Points of Concurrency – FILL IN THE BLANK
Fill in the blank with “inside”, “outside”, or “on”
1. The centroid of an acute triangle can be found _________ the triangle.
2. The point of concurrency of perpendicular bisectors of a right triangle can be
found ____________ the triangle.
3. The point of concurrency of the altitudes of an obtuse triangle can be
found __________ the triangle.
4. The incenter of an obtuse triangle can be found ___________ the triangle.
5. The incenter of an acute triangle can be found ____________ the triangle.
Section 6: Points of Concurrency – centroids and circumcenters
B. G is the centroid. Suppose AD = 21. What is the measure of AG?
C
B
G
D
P. Using the information from the basic problem above,
what is the length of GD?
A
F
E
A. Find the center of the circle that you can circumscribe about ABC.
A (-1, -4) B(3, -4), C(-1, 0)
Section 7: Inequalities
Solve the following inequalities.
B. 2x – 10 + 3x < 10
P.
-3(x + 4) < 3
A. 2x + 4 < 13x -1
Section 8: Triangle Inequalities
B.
a. List the angles of BCD from smallest to largest.
BC = 2, CD = 5.2 , BD = 3.3
b. List the sides of PBJ from shortest to longest.
P. Is it possible for a triangle to have sides with the given lengths? Explain why or why not.
3 ft, 6 ft, 8 ft
A.
Explain how m<2 > m< 3.
4
3
6
5
1
2