Test - Review

Name: ________________________ Class: ___________________ Date: __________
ID: A
UNIT 6 TEST REVIEW
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1
Where can the lines containing the altitudes of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A) I, II, or II
B) I only
C) I or II only
D) III only
2
Find the value of x. The diagram is not to scale.
Given: RS ≅ ST , m∠RST = 5x − 54, m∠STU = 7x
A) 16
3
B) 14
C) 124
D) 19
Use the information in the diagram to determine the measure of the angle formed by the line from the point on
the ground to the top of the building and the side of the building. The diagram is not to scale.
A) 108º
B) 54º
C) 27º
D) 36º
4
Where is the circumcenter of any given triangle?
A) the point of concurrency of the altitudes of the triangle
B) the point of concurrency of the medians of the triangle
C) the point of concurrency of the perpendicular bisectors of the sides of the triangle
D) the point of concurrency of the bisectors of the angles of the triangle
5
Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A) I only
B) I, II, or II
C) II only
D) I or II only
1
Name: ________________________
6
Find the length of the midsegment. The diagram is not to scale.
A) 52
7
8
B) 26
C) 10.5
Find the circumcenter of ∆EFG with E(6, 4), F(6, 0), and G(8, 0).
A) (6, 2)
B) (2, 7)
C) (7, 2)
D) 14
D) (2, 0)
Name a median for ∆ABC.
A) BD
9
ID: A
B) AF
C) AD
D) CE
The legs of an isosceles triangle have lengths x + 3 and −x + 15. The base has length x + 1. What is the length
of the base?
A) 6
C) 7
B) 9
D) cannot be determined
10 In ∆ACE, G is the centroid and BE = 15. Find BG and GE.
3
1
4
4
B) BG = 5, GE = 10
A) BG = 3 , GE = 11
1
1
2
2
D) BG = 10, GE = 5
C) BG = 7 , GE = 7
2
Name: ________________________
ID: A
11 In ∆ABC, centroid D is on median AM . AD = x + 6 and DM = 3x − 2. Find AM.
A) 12
B) 13
C) 6
D) 2
12 Find the value of x. The diagram is not to scale.
A) x = 50
B) x = 22
C) x = 14
D) none of these
13 Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
A) 140 ft
B) 70 ft
C) 35 ft
D) 33 ft
14 Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A) I only
B) I, II, or II
C) I or III only
D) III only
15 Two sides of an equilateral triangle have lengths 2x − 3 and x − 1. Which could be the length of the third
side: 3 − x or 5x − 1?
A) 3 – x only
B) both 3 – x and 5x – 1
C) 5x – 1 only
D) neither 3 – x nor 5x – 1
16 For which situation could you immediately prove ∆1 ≅ ∆2 using the HL Theorem?
A) III only
B) II and III
C) II only
3
D) I only
Name: ________________________
ID: A
17 Find the values of x and y.
A) x = 90, y = 70
B) x = 90, y = 20
C) x = 70, y = 20
D) x = 20, y = 70
18 Name the point of concurrency of the angle bisectors.
A) A
B) C
C) B
D) not shown
19 ∆ABC has vertices A(4,4),B(−1,4), and C(−1,−7). Find the orthocenter of ∆ABC.
A) (1.5,−1.5)
C) (−1,−7)
B) (4,4)
D) (−1,4)
20 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
A) circumcenter
B) circumcenter
incenter
incenter
orthocenter
centroid
centroid
orthocenter
C) incenter
circumcenter
orthocenter
centroid
D) incenter
circumcenter
centroid
orthocenter
21 Where can the medians of a triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A) III only
B) I only
C) I or III only
4
D) I, II, or II
Name: ________________________


→
22
ID: A


→
BE is the bisector of ∠ABC and CD is the bisector of ∠ACB. Also, ∠XBA ≅ ∠YCA. Which of AAS, SSS,
SAS, or ASA would you use to help you prove BL ≅ CM ?
A) SAS
B) ASA
C) AAS
D) SSS
B) 7
C) 5
D) 8
23 Find the value of x.
A) 7.6
24 T is the midpoint of QR. U is the midpoint of QS. m∠QRS=60 and m∠QUT = 85. What are m∠QTU,
m∠RTU, m∠QSR m∠TUS, and m∠TQU? Explain.
5
Name: ________________________
ID: A
25 Supply the missing reasons to complete the proof.
Given: ∠P ≅ ∠S and PR ≅ SR
Prove: QR ≅ TR
Statement
1. ∠P ≅ ∠S and
Reasons
1.
PR ≅ SR
2. ∠QRP ≅ ∠TRS
2.
3. ∆QRP ≅ ∆TRS
3.
4. QR ≅ TR
4.
6
Name: ________________________
ID: A
26 Write a two-column proof.
Given: SD ⊥ HT; SH ≅ ST
Prove: ∆SHD = ∆STD
Statement
1.
Reason
1.
2.
3.
4.
5.
2.
3.
4.
5.
27 B is the midpoint of AC and D is the midpoint of CE. Solve for x, BD, and AE given BD = 5x + 2 and
AE = 4x + 10.
7

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