Geometry

3 Chapter Test M athX

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Do you know HOW? Use the given information to write an equation of
Find the measure of the third angle of a triangle given each line.
the measures of two angles.
14. slope -5, y-intercept -2
1. 57 and 101 15. slope 12, passes through (4, -1)
16. passes through (1, 5) and (3, 11)
2. 72 and 72

3. x and 20 Algebra  Find the value of x for which O } m.

Find mj1 and mj2. Justify each answer. 17. 18. ᐍ

4. 5. 85Њ (14x Ϫ 5)Њ
1 ᐍ
21 (2x Ϫ 30)Њ m
65Њ 70Њ 2 13xЊ 45Њ
m xЊ

Graph each pair of lines. Tell whether they are parallel,

6. 85Њ 7. perpendicular, or neither.

hsm11gmse_03ca_t00535.ai 19. yh=sm4x1+1g7mansde_y0=3-ca41_xt0-03539h.sami 11gmse_03ca_t00540.ai

12 hsm111gms2e_7003Њ ca_t00536.a 2i0. y = 3x - 4 and y = 3x + 1

21. y = x + 5 and y = -5x - 1

8. Draw a line m and a point T not on the line. Do you UNDERSTAND?

Construct the line through T perpendicular to m. 22. Developing Proof  Provide the reason for each step.

9. sDhosratmhwa1at1nmgym}∠<BsACeB>_.C0.3Tchaen_tc0o0n5st3r7uhc.atsilmin1e1mgtmhrsoeu_g0h3Aca_t00538 .ai GPrivoevne::   / } m, ∠2 ≅ ∠4
n}p

10. The measures of the angles of a triangle are 2x, Statements Reasons

x + 24, and x - 4. Find the value of x. Then find 1) / } m 1) a. ? ᐍm
the measures of the angles.
2) ∠1 ≅ ∠2 2) b. ? 1 2
n

Determine whether the following are parallel lines, 3) ∠2 ≅ ∠4 3) c. ? 43 p
skew lines, or neither. 4) ∠1 ≅ ∠4 4) d. ?

11. opposite sides of a rectangular picture frame 5) n } p 5) e. ?

12. the center line of a soccer field and a sideline of 23. Reasoning  Suppose a line intersecting two planes A
the field
and B forms a right angle at exactly one point in each
13. the path of an airplane flying north at 15,000 ft and
the path of an airplane flying west at 10,000 ft plane. What must be true about planes A and B?
hsm11gmse_03ca_t00541.a
(Hint: Draw a picture.)

Chapter 3  Chapter Test 211

3 Common Core Cumulative ASSESSMENT
Standards Review

Some test questions ask you to In the diagram, q } r and s # t. If TIP 1
analyze a diagram. Read the m∠1 = 35, what is m∠3?
sample question at the right. Use m∠1 and what you know
Then follow the tips to answer it. ts about the measures of angles
q2 formed by perpendicular
TIP 2 lines to find m∠2.
1
Use the diagram to find Think It Through
the relationship between r
∠2 and ∠3. 3 Since s # t, the angle formed by
∠1 and ∠2 is a right angle. So
35 55 m∠1 + m∠2 = 90. Substitute
45 90 35 for m∠1 and solve for m∠2.

hsm11gmse_03cu_t00543.ai m∠2 = 90 - 35 = 55
∠2 and ∠3 are alternate
exterior angles. Since q } r,
∠2 ≅ ∠3. So m∠3 = 55. The
correct answer is C.

VLVeooscsacoabnubluarlayry Builder Selected Response

As you solve test items, you must understand the Read each question. Then write the letter of the correct
meanings of mathematical terms. Match each term answer on your paper.
with its mathematical meaning.
1. Which expression describes the area of a square that
has side lengths 7n3?
A . transversal I. two angles whose measures
14n6 49n6
B. complementary have sum 90
14n9 49n9
angles II. a point that divides a

C . conditional segment into two congruent 2. What is the area of △PQR?
segments
Q 4y
D. midpoint III. an if-then statement 2

E. asunpgplelsementary IV. caolipnleanthaar tliinnetesrastetcwtsotdwiostinct Ϫ4 O x
P Ϫ2 3
points R

V. two angles whose measures
have sum 180

10 units2 20 units2

15 units2 25 units2

hsm11gmse_03cu_t00544.ai

212 Chapter 3  Common Core Cumulative Standards Review

3. Which condition(s) will allow you to prove that / } m? 9. Given the diagram below, which expression could be
used to find the sum of the angles in the triangle?

1 ᐍ ab c g
23 m de f
45

I. ∠1 ≅ 4 f+g+c
a + b + c
II. ∠2 ≅ ∠5 a + bg+eoem12_se_ccr_c03_csr_003.ai
d + e + g
III. ∠3 ≅hs∠m411gmse_03cu_t00545.ai
1 0. What is the value of x in the figure?
IV. m∠2 + m∠4 = 180

III only II and III only 130Њ

I and IV only I, II, III, and IV

4. The length of your rectangular vegetable garden 2xЊ
is 15 times its width. You used 160 ft of fencing to
surround the garden. How much area do you have 20 45
25 50
for planting?

150 ft2 800 ft2 1 1. The net for a cyhlinsmdr1ic1agl cmonstea_in0e3rctuha_tth0o0l5d4s 6a.satiack of

375 ft2 1600 ft2 DVDs is shown below. What is the total area of the net?

5. Which of the following angle relationships can you use 6 cm 8 cm
to prove that two lines are parallel? 6 cm

supplementary corresponding angles 226 cm2 528 cm2
302 cm2 582 cm2
congruent alternate interior angles

congruent vertical angles

congruent same-side interior angles

6. Which point lies farthest from the origin? 1 2. What are the coohrdsimna1te1sgomf tshee_m0i3dcpuo_intt0o0f5a4s7e.gami ent

(0, -7) ( -4, -3) with endpoints ( -1, 2) and (5, 6)?

( -3, 8) (5, 1) (2, 4) (6, 4)

7. ∠A and ∠B are supplementary vertical angles. What (4, 8) (3, 4)
is m∠B?
13. What is the measure of any exterior angle of an
45 135
equiangular triangle?
90 180
30 90

8. Which types of angles can an obtuse triangle have? 60 120

I. a right angle II. two acute angles

III. an obtuse angle IV. two vertical angles

I and II III and IV

II and III I and IV

Chapter 3  Common Core Cumulative Standards Review 213

Constructed Response 2 0. Is your friend’s argument for the following situation
valid? Explain.
1 4. What is the measure of ∠1?
Given:  If you buy a one-year membership at the gym,
1 then you get one month free. You got a free
month at the gym.
120Њ 78Њ
Your frie nd’s conclusion:  You bought a one-year
1 5. Two angles of an isosceles triangle have measures membership.
54.5 and 71. Whgeaotmi1s2t_hsee_cmcr_ec0a3s_ucsrre_0o01f.atihe third angle?
2 1. Draw MN . Then construct the perpendicular bisector
1 6. In the <cCoDo>rcdoinntaatienpsl(a6n,ey,)<AaBn>dc(o1n2t,a1in0)s.(F-o2r,w-h4a)t and of MN .
(6, 8). value
2 2. What is the equation for a line that passes through the
point (3, -3) and is parallel to the line shown in the
graph below?

of y are the lines parallel? y
4
17. A circular wading pool has a diameter of 10 ft. What
is the circumference of the wading pool in feet? 2
Use 3.14 for p.
Ϫ4 Ϫ2 O 2 x
Ϫ2 4

18. What is the measure of the complement of a Ϫ4
56° angle?

19. A new athletic field is being constructed, as shown Extended Response
below. The given coordinates are in terms of yards. geom12_se_ccr_c03_csr_002.ai
What is the area of the field in square yards?
2 3. CD has endpoints C(5, 7) and D(10, -5). What are the
y (10, 80) (110, 80) coordinates of the midpoint of CD? What is CD? Show
your work.

24. Examples and nonexamples of bleebles are shown.

Bleebles Not bleebles

(10, 20) (110, 20) x
O

hsm11gmse_03cu_t00550.ai

a. Is the figure at the right a

bleeble? Explain your reasoning.

bh. sWmh1a1t gisma dseef_in0i3ticoun_fot0r 0bl5e4eb9l.ea?i

hsm11gmse_03cu_t00551.a

214 Chapter 3  Common Core Cumulative Standards Review