Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry - Chapter 5 - Corrective #1 15-16
Short Answer
1. Tell if the measures 8, 10, and 9 can be side lengths of a triangle. If so, classify the triangle as acute, right, or
obtuse.
2. Find the value of n in the triangle.
3. The lengths of two sides of a triangle are 5 inches and 7 inches. Find the range of possible lengths for the
third side, s.
4. Vanessa wants to measure the width of a reservoir. She measures a triangle at one side of the reservoir as
shown in the diagram. What is the width of the reservoir (BC across the base)?
5. AO and DO are the angle bisectors of ∠DAB and ∠BDA, respectively. CD ≅ BD ≅ AB, and m∠C = 40°.
Find m∠BAO.
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6. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width
to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27"
TV screen?
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
7. Each triangle is a 45°-45°-90° triangle. Find the value of x.
a.
x=
3
b.
x=
3
3
2
c.
x=3 2
d.
x=
3
2
8. Consider the points A(−2, 5), B(2, − 3) , C(8, 0), and P(4, 3) . P is on the bisector of ∠ABC . Write an
equation of the line in point-slope form that contains the bisector of ∠ABC .
1
a. y − 4 = 3 (x − 3)
c. y − 4 = 3(x − 3)
b.
____
2
2
y − 3 = 3(x − 4)
d.
y − 3 = 3 (x − 4)
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9. Find the orthocenter of ∆ABC with vertices A(1, − 3), B(2, 7), and C(−2, − 3).
Ê
Ê
17 ˆ
16 ˆ
a. ÁÁÁ 2, − 5 ˜˜˜
c. ÁÁÁ 2, − 5 ˜˜˜
Ë
¯
Ë
¯
ÊÁ
ÊÁ
11 ˆ
13 ˆ
˜
b. ÁÁ 2, − 5 ˜˜
d. ÁÁ 2, − 5 ˜˜˜
Ë
¯
Ë
¯
2
____ 10. Danny and Dana start hiking from the same base camp and head in opposite directions. Danny walks 6 miles
due west, then changes direction and walks for 5 miles to point C. Dana hikes 6 miles due east, then changes
direction and walks for 5 miles to point S. Use the diagram to find which hiker is farther from the base camp.
a.
b.
c.
d.
Danny is farther from the base camp than Dana.
There is not enough data to answer the question.
Both hikers are the same distance from the base camp.
Dana is farther from the base camp than Danny.
____ 11. An architect designs the front view of a house with a gable roof that has a 45°-45°-90° triangle shape. The
overhangs are 0.5 meter each from the exterior walls, and the width of the house is 16 meters. What should
the side length l of the triangle be? Round your answer to the nearest meter.
a.
b.
23 m
12 m
c.
d.
24 m
11 m
____ 12. Tell whether a triangle can have sides with lengths 3, 4, and 8.
a. No
b. Yes
Matching
Match each vocabulary term with its definition.
a. hypotenuse
b. equidistant
c. midsegment of a triangle
d. altitude of a triangle
e. leg of a triangle
f. centroid of a triangle
g. median of a triangle
____ 13. a perpendicular segment from a vertex to the line containing the opposite side
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____ 14. a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
____ 15. a segment that joins the midpoints of two sides of the triangle
____ 16. the same distance from two or more objects
____ 17. the point of concurrency of the three medians of a triangle
Match each vocabulary term with its definition.
a. concurrent
b. circumscribed
c. incenter of a triangle
d. circumference
e. orthocenter of a triangle
f. inscribed
g. circumcenter of a triangle
____ 18. for a figure to be drawn within another figure in which every vertex of the enclosed figure lies on or is
tangent to the outer figure
____ 19. for a figure to be drawn around another figure in which every vertex of the enclosed figure lies on or is
tangent to the outer figure
____ 20. the point of concurrency of the three angle bisectors of a triangle
____ 21. the point of concurrency of the three altitudes of a triangle
____ 22. the point of concurrency of the three perpendicular bisectors of a triangle
Match each vocabulary term with its definition.
a. locus
b. concurrent
c. point of concurrency
d. equidistant
e. focus
f. Pythagorean triple
g. indirect proof
____ 23. a point where three or more lines coincide
____ 24. three or more lines that intersect at one point
____ 25. a set of points that satisfies a given condition
____ 26. a proof in which the statement to be proved is assumed to be false and a contradiction is shown
____ 27. a set of three nonzero whole numbers a, b, and c such that a 2 + b 2 = c 2
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ID: A
Geometry - Chapter 5 - Corrective #1 15-16
Answer Section
SHORT ANSWER
1. ANS:
Yes; acute triangle
TOP: 5-7 The Pythagorean Theorem
2. ANS:
11
TOP: 5-4 The Triangle Midsegment Theorem
3. ANS:
2 < s < 12
TOP: 5-5 Indirect Proof and Inequalities in One Triangle
4. ANS:
300 m
TOP: 5-4 The Triangle Midsegment Theorem
5. ANS:
m∠BAO = 10°
TOP: 5-2 Bisectors of Triangles
6. ANS:
width: 21.6 in., height: 16.2 in.
TOP: 5-7 The Pythagorean Theorem
MULTIPLE CHOICE
7.
8.
9.
10.
11.
12.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
B
A
A
B
A
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
5-8 Applying Special Right Triangles
5-1 Perpendicular and Angle Bisectors
5-3 Medians and Altitudes of Triangles
5-6 Inequalities in Two Triangles
5-8 Applying Special Right Triangles
5-5 Indirect Proof and Inequalities in One Triangle
D
G
C
B
TOP:
TOP:
TOP:
TOP:
5-3 Medians and Altitudes of Triangles
5-3 Medians and Altitudes of Triangles
5-4 The Triangle Midsegment Theorem
5-1 Perpendicular and Angle Bisectors
MATCHING
13.
14.
15.
16.
ANS:
ANS:
ANS:
ANS:
1
ID: A
17. ANS: F
TOP: 5-3 Medians and Altitudes of Triangles
18.
19.
20.
21.
22.
ANS:
ANS:
ANS:
ANS:
ANS:
F
B
C
E
G
TOP:
TOP:
TOP:
TOP:
TOP:
5-2 Bisectors of Triangles
5-2 Bisectors of Triangles
5-2 Bisectors of Triangles
5-3 Medians and Altitudes of Triangles
5-2 Bisectors of Triangles
23.
24.
25.
26.
27.
ANS:
ANS:
ANS:
ANS:
ANS:
C
B
A
G
F
TOP:
TOP:
TOP:
TOP:
TOP:
5-2 Bisectors of Triangles
5-2 Bisectors of Triangles
5-1 Perpendicular and Angle Bisectors
5-5 Indirect Proof and Inequalities in One Triangle
5-7 The Pythagorean Theorem
2