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
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
254
Holt McDougal Geometry