1.
Use the diagram below to answer the question. The diagram is not to scale.
A length of rope is stretched between the top edge of a building and a stake in the ground. The rope also touches the top of a tree between the stake and the building at a 48º angle. What angle is formed by the rope and the building? (1point)
· 138°
· 52°
· 42°
· 48°
2.
Which statement can you conclude is true from the given information?
Given:the perpendicular bisector of .
(1point)
· IAK is a right angle.
· BI = BK
· B is the midpoint of .
· BK = AK
3.
Find the circumcenter of EFG with E(2, 6), F(2, 4), and G(6, 4). (1point)
· (7, 4)
· (5, 4)
· (4, 5)
· (2, 7)
4.
Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle (1point)
· I only
· III only
· I or III only
· I, II, or III
5.
What is the name of the segment inside of the large triangle?
(1point)
· perpendicular bisector
· altitude
· median
· angle bisector
6.
mA = 8x –2, mB = 2x – 8, and mC = 94 – 4x. List the sides of ABC in order from shortest to longest. (1point)
· ; ;
· ;;
· ;;
· ; ;
7.
Which three lengths could be the lengths of the sides of a triangle? (1point)
· 6 cm, 23 cm, 11 cm
· 10 cm, 15 cm, 24 cm
· 22 cm, 6 cm, 6 cm
· 15 cm, 9 cm, 24 cm
8.
Which of the following must be true? The diagram is not to scale.
(1point)
· BC < FH
· AC = FH
· AB < BC
· AC < FH
9.
List the sides in order from shortest to longest. The diagram is not to scale.
(1point)
· , ,
· ,,
· ,,
· , ,
10.
The lengths of two sides of a triangle are 9 and 15. What can be said about the length of the third side? (1point)
· It must be greater than or equal to 6 and less than 24.
· It must be greater than or equal to 6 and at most 24.
· It must be greater than 6 and less than 24.
· It must be greater than 6 and at most 24.
11.
Name the smallest angle of ABC. The diagram is not to scale.
(1point)
· C
· A
· Two angles are the same size and smaller than the third.
· B
Fill in the Blank
12.
The ______of a triangle is a segment that connects the midpoints of two sides of the triangle. (1point)
13.
A point is ______from two objects if it is the same distance from the objects. (1point)
14.
The distance from a point to a line is the length of the ______segment from the point to the line. (1point)
15.
When three or more lines intersect at one point, they are ______. (1point)
WO
16.
WorkPad
Note: Remember to show all of the steps that you use to solve the problem for questions 16–20. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer.
What is the range of possible values for x? The diagram is not to scale.
(3points)
17.
B is the midpoint of and D is the midpoint of . Solve for x, given BD = 3x + 5 and AE = 4x + 20.
(2points)
18.
In ACE, G is the centroid and BE = 9. Find BG and GE.
(3points)
19.
bisects EDG. Find FG. The diagram is not to scale.
(3points)
20.
ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter, including any necessary points or slopes you had to derive. (3points)
Short Answer
Note:Your teacher will grade your response to questions 20–23 to ensure you receive proper credit for your answer.
21.
For a triangle, list the respective names of the points of concurrency of
· perpendicular bisectors of the sides
· bisectors of the angles
· medians
· lines containing the altitudes
(4points)
22.
What are the properties of the circumcenter of a triangle? (2points)
23.
What are the properties of the incenter of a triangle? (2points)