1. No category

Name ________________________________________ Date ___________________ Class __________________
Chapter
5
Properties and Attributes of Triangles
Cumulative Test
8. Where is the image of (−6, 2) reflected
across the graph of y = −x?
Choose the best answer.
HJJG
1. Which of PQ and QR contains P?
A PQ only
HJJG
B QR only
D Neither
G 8
J 13
JJJG
3. SU bisects ∠RST. If m∠RST = (8x + 15)�
and m∠RSU = 5x�, what is m∠RST?
C 50�
B 37.5�
D 75�
H 112�
G 78�
J 158�
C 16 m2
B 8 m2
D 64 m2
H 6π cm2
G 2.25π cm2
J 36π cm2
C (2.5, 0.5)
B (4, 17)
D (0.5, 5.5)
B −3
D 9
J If the car will not start, then it is out
of gas.
11. For which conditional statement (p → q)
is its inverse (∼p → ∼q) false?
A If a point is a midpoint of a segment,
then it divides the segment into two
congruent segments.
B If Mike does not become an airplane
pilot, then he will not learn how to fly
a plane.
C If you see a zebra, then you must be
in a zoo.
D If the biggest holiday of the month is
Thanksgiving, then the month is
November.
12. Which justifies the statement?
If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then
∠1 ≅ ∠3.
7. The midpoint of a segment is (2, −5), and
one of the endpoints is (3, 6).
Where is the other endpoint?
A (1, −16)
C 3
H If the day is between Monday and
Wednesday, then it is Tuesday.
6. What is the area of a circle whose
diameter is 3 centimeters?
F 1.5π cm2
A −9
G If Meg lives in Egypt, then she lives
in Africa.
5. The perimeter of a square is 8 meters.
What is its area?
A 4 m2
J (−2, 6)
F If a fruit has seeds inside, then it is
an orange.
4. If the complement of an angle measures
22�, what is the measure of its
supplement?
F 68�
G (−2, −6)
10. For which conditional statement (p → q)
is its converse (q → p) false?
H 9
A 25�
H (2, 6)
9. What is the next term in the sequence?
729, −243, 81, −27, . . .
C Both
2. K is between J and L. JK = 3x − 5, and
KL = 2x + 1. If JL = 16, what is JK?
F 7
F (2, −6)
F Transitive Property of Congruence
G Substitution
H Symmetric Property of Congruence
J Reflexive Property of Congruence
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101
Holt McDougal Geometry
Name ________________________________________ Date ___________________ Class __________________
Chapter
5
Properties and Attributes of Triangles
Cumulative Test continued
13. Which is the most logical conclusion by
the Law of Syllogism?
If one of the angles of a triangle is
obtuse, then the other two angles are
acute. If a triangle is an obtuse triangle,
then one of its angles is obtuse. A
triangle has two acute angles.
16. Complete the statement.
Two lines are parallel if the same-side
interior angles are _______ angles.
F complementary
G supplementary
H congruent
J corresponding
A The triangle is obtuse.
17. Which angles are alternate interior
angles?
B The other angle in the triangle is
obtuse.
C The triangle is not obtuse.
D None of these are valid conclusions.
14. Which is a true biconditional statement?
F Four points are coplanar if and only if
they are noncollinear.
G Two angles are complementary if
and only if the sum of their measures
is 90�.
J A figure has an endpoint if and only if
the figure is a segment.
Reasons
1. Given
2. x + 5 = 0
2. Add. Prop. of =
3. 2(x � 5) = 0
3.
B ∠1 and ∠5
D ∠3 and ∠7
Statements
15. Complete the proof.
Given: x = −5
Prove: 2(x + 5) = 0
Proof:
1. x = −5
C ∠3 and ∠4
18. Complete the proof.
Given: k � �
Prove: ∠1 and ∠6
are supplementary.
Proof:
H A side of a triangle is a hypotenuse if
and only if it is the longest side of a
triangle.
Statements
A ∠1 and ∠4
?
A Multiplication Property of Equality
B Transitive Property of Equality
Reasons
1. k � �
1. Given
2. ∠1 ≅ ∠5
2.
3. m∠1 = m∠5
3. Def. of ≅
4. ∠5 and ∠6 are
supplementary.
4. Linear Pair Thm.
5. m∠5 + m∠6 = 180�
5. Def. of supp. �
6. m∠1 + m∠6 = 180�
6. Subst.
7. ∠1 and ∠6 are
supplementary.
7. Def. of supp. �
?
F Alternate Exterior Angle Theorem
C Subtraction Property of Equality
G Alternate Interior Angle Theorem
D Reflexive Property of Equality
H Same-Side Interior Angle Theorem
J Corresponding Angle Theorem
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102
Holt McDougal Geometry
Name ________________________________________ Date ___________________ Class __________________
Chapter
5
Properties and Attributes of Triangles
Cumulative Test continued
19. A line passes through the points (5, −8)
and (6, 2). What is the slope?
1
A −10
C
10
6
B −
D 10
11
24. Three sides of a triangle are shown.
Which triangle is acute?
F 3, 4, 5
H 4, 5, 6
G 5, 12, 13
J 4, 7, 10
25. Find y.
20. Complete the paragraph proof.
Given: ∠2 ≅ ∠5
Prove: ∠1 ≅ ∠4
F m∠2 + m∠3 = 180�
G m∠4 + m∠7 = 180�
J m∠6 + m∠7 = 180�
21. Find all values for x.
B 0 < x < 11
D x > −3
B 82�
D 134�
F (–10, 1)
H (–0.4, 1)
G (–10, 5)
J (–0.4, 0.2)
27. Complete the statement.
If ∠U ≅ ∠P, ∠S ≅ ∠Q, ∠T ≅ ∠R,
UT ≅ PR, US ≅ PQ, and ST ≅ QR , then
�PQR ≅ _______.
H m∠4 + m∠5 = 180�
C 4 < x < 11
C 128�
26. Point R in ∆QRS has coordinates (–2, 1).
∆QRS underwent a dilation with scale
factor 5 centered at the origin. What are
the coordinates of the image of R?
Proof:
It is given that ∠2 ≅ ∠5. By the Linear
Pair Theorem, m∠2 + m∠1 = 180�
and _______. By the Congruent
Supplements Theorem, ∠1 ≅ ∠4.
A x < 11
A 36�
A �RQP
C �TUS
B �STU
D �UST
28. What is the least information needed to
prove the triangles congruent by SSS?
22. What is the slope of the line
3
perpendicular to y = − x + 9?
2
3
2
F
H −
2
3
3
2
J −
G
2
3
F ∠M ≅ ∠Q
H LN ≅ PR and
MN ≅ QR
G LN ≅ PR
23. What is the equation of the line that
passes through (0, −2) and (4, 6)?
A y = 2x − 2
C y=x−2
1
B y = x −2
D y = −2x + 2
2
J LN ≅ QR and
MN ≅ PR
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103
Holt McDougal Geometry
Name ________________________________________ Date ___________________ Class __________________
Chapter
5
Properties and Attributes of Triangles
Cumulative Test continued
JJJG
33. QS bisects ∠PQR. What is QR?
29. Why is �PQS ≅ �RQS?
A SAS
B ASA
A 65
B 50
C AAA
D HL
30. Complete the proof.
Given: �ABC is equilateral, and
BD is an altitude.
C 40
D 15
34. XL, XM, and XN are perpendicular
bisectors. The perimeter of ΔFGH is 54.
What is FG?
Prove: BD bisects AC.
F 36
G 27
Proof:
35. SV and RT are medians. What is
JS − JT?
By definition of equilateral, AB ≅ CB,
and by the Reflexive Property of
Congruence, BD ≅ BD . Since BD
is an altitude, ∠BDA and ∠BDC are
right angles. So �BDA and �BDC are
right � and �BDA ≅ �BDC by HL.
Therefore, AD ≅ CD by ? . By
definition of bisector, BD bisects AC.
F HL
H ASA
G SAS
J CPCTC
G right
J equiangular
C 2y −
B 2x − 3y
D
1
x
2
1
x − 2y
2
37. Two sides of a 30�-60�-90� triangle are 9
and 18. What is the length of the third
side?
A 9 2
C 18 2
B 9 3
D 18 3
38. PQ is a midsegment. What is PQ?
32. One of the base angles of an isosceles
triangle is 40�. Which is the triangle
classification according to its angles?
H obtuse
A x−y
36. In ΔJKL, JK > JL > KL. Which is the
correct order of the angles from smallest
measure to largest?
F ∠J , ∠L , ∠K
H ∠K, ∠L, ∠J
G ∠J, ∠K, ∠L
J ∠L, ∠K, ∠J
31. Given: TUVW is a rectangle.
Prove: TV = UW
For an analytic proof, which is the
best placement of the rectangle in the
coordinate plane?
A T(0, 0), U(a, b), V(0, c), W(−a, c − b)
B T(0, 0), U(a, 0), V(a, b), W(0, b)
C T(a, b), U(a + b, 0), V(a + b, c), W(0, c)
D T(0, 0), U(a, 0), V(a, a), W(0, a)
F acute
H 18
J 9
F 16
G 17
H 32
J 34
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104
Holt McDougal Geometry
11. False
Performance Assessment
12. KM, KL, LM
1. Perpendicular Bisector Theorem
13. 6 < x < 10
2. B is the midpoint of AC since BE is a
midsegment.
14. 24
3. 90°; Def. of perpendicular bisector
15. The lengths do not form a Pythagorean
triple because the hypotenuse ( 34 ) is
not a whole number.
4. ∠BDC, ∠DBE, ∠EDB, ∠ABE, ∠A
5. AE < AB; ∠AEB = 90°, ∠ABE = 45°,
and, if two angles in a triangle are
not congruent, then the longer side
is opposite the larger angle.
16. obtuse
17. 6
18. 10
6. The triangles are not congruent. The
reasoning in the answer for question 5
can be used to show that AB > AE and
AB > EB and likewise that DC > BC.
But since AB = BC, it follows that DC is
longer than each side of �ABE.
Therefore �ABE cannot be congruent
to �CDB.
Chapter Test Form C: Free Response
1. 56°
2. y − 3 = 2(x − 4)
3. 72° or 8°
⎛ 1⎞
4. ⎜ 4, ⎟
⎝ 2⎠
5. m∠VGT = 108°; the distance from G to
UV = 19.5
7. a. 14
b. 14 2, or about 19.8
c. 28
d. 28 2, or about 39.6
6. (1, 1)
7. (4, 4)
Cumulative Test
8. 4 or −3
9. 132°
10. Let �ABC be an obtuse triangle with
∠A as its obtuse angle. Suppose �ABC
has a right angle, say ∠B. Since m∠A >
90° and m∠B = 90°, and since it must
be true that m∠C > 0°, it follows that
m∠A + m∠B + m∠C > 180°. This last
inequality contradicts the Triangle Sum
Theorem. The assumption that m∠B =
90° is therefore false. Hence the obtuse
triangle cannot have a right angle.
11. 5 < s < 19
12. ∠M, ∠L, ∠K
13. 3 < x < 10
14. 9, 12, and 15
15. True
16. 2 < x < 4 3
17. 24 cm
2
2
18. 288 3 in or about 498.8 in
1. C
20. H
2. F
21. C
3. D
22. G
4. H
23. A
5. A
24. H
6. G
25. B
7. A
26. G
8. J
27. D
9. D
28. H
10. G
29. B
11. C
30. J
12. F
31. B
13. D
32. H
14. G
33. A
15. A
34. H
16. G
35. C
17. D
36. G
18. F
37. B
19. D
38. G
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254
Holt McDougal Geometry