Download GEOMETRY PRACTICE Test 2 (3.5-3.6) Answer

GEOMETRY
PRACTICE
Test 2
(3.5-3.6)
SHOW ALL WORK TO PROVE ANSWERS
1. Find the value of the variable if
and
not to scale.
1
2
3
The diagram is
6. Find the missing angle measures. The diagram is not
to scale.
l
4
112°
x°
120° y°
5
6
7
79°
m
8
2. The sum of the measures of two exterior angles of a
triangle is 277. What is the measure of the third
exterior angle?
7. The jewelry box has the shape of a regular pentagon.
It is packaged in a rectangular box as shown here.
The box uses two pairs of congruent right triangles
made of foam to fill its four corners. Find the
measure of the foam angle marked.
SHOW ALL work to earn credit.
3. Find
. The diagram is not to scale.
96°
118°
115°
x
104°
x
A
4. A nonregular hexagon has five exterior angle
measures of 55, 58, 69, 57, and 55. What is the
measure of the interior angle adjacent to the sixth
exterior angle?
5. How many sides does a regular polygon have if each
exterior angle measures 72?
8. Find the measures of an interior angle and an
exterior angle of a regular polygon with 6 sides.
9. Write the equation 9x + 3y = –9 in slope-intercept
form. Then graph the line.
The diagram is not to scale.
10. Write a two-column proof.
Given:
Prove:
11.
q
5
1
3 4
2
p
4
137 o
6
5 6
7 8
r
1
2
11. Find the measure of each interior and exterior angle
of the figure on the right.
12. Identify the form of the equation –3x – y = –2. To
graph the equation, would you use the given form or
change to another form? Explain.=
8
3
13. Explain how to tell whether a polygon is convex.
14. Which statement is false? Explain.
A. An equiangular polygon has all angles congrue B.
A regular polygon is both equilateral and
equiangular.
C. An equilateral polygon has all sides congruent.
D. A polygon is concave if no diagonal contains
points outside the polygon.
.
9
7
15. Write a two-column proof.
Given:
Prove:
are supplementary.
1
2
3
l
4
5
6
7
16. For a regular n-gon:
a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior
angles, one at each vertex?
d. What is the measure of each exterior angle.
e. Find the sum of your answers to parts b and d.
Explain why this sum makes sense.
18. Graph
.
19. The Polygon Angle-Sum Theorem states: The sum
of the measures of the angles of an n-gon is ____.
20. Complete this statement. A polygon whose sides all
have the same length is_____
21. Complete this statement. A polygon whose sides all
have the same length and angles have the same
measure is_____.
22. Write an equation in point-slope form then write in
slope-intercept form of the line through point P(–4,
6) with slope –3.
8
m
117. Complete this statement. The sum of the measures
oof the exterior angles of an n-gon, one at each vertex, is
____.
23. Complete this statement. A polygon whose angles
all have the same measure is ____.
24. At the curb a ramp is 13 inches off the ground. The
other end of the ramp rests on the street 91 inches
straight out from the curb.
25. Write an equation in slope-intercept form of the line
through points S(–2, –6) and T(4, 3).
26. Graph the line that goes through point (–2, 2) with
3
slope .
5
27. Write an equation in point-slope form, y – y1 = m(x –
x1), of the line through points (5, –2) and (2, 10) Use
(5, –2) as the point (x1, y1).
b.
28. Write a two-column proof.
6
y
4
Given:
Prove:
and
a
are supplementary.
b
c
2
–6 –4 –2
–2
r
d
2
4
6 x
2
4
6 x
2
4
6 x
–4
e
–6
f
g
s
h
c.
6
y
4
2
29. Write a two-column proof?
Given:
Prove:
and
–6 –4 –2
–2
–4
are supplementary.
–6
K
A
d.
B
J
C D
6
y
4
2
E F
G H
L
–6 –4 –2
–2
–4
–6
5
30. Graph y =  x – 1.
4
31. Write an equation in point-slope form of the line
through point K(–1, 6) with slope –4.
32. Write an equation for the vertical line that contains
point E(10, 1).
33. Write the equation for EACH graph
a.
34. Find the x- and y- intercepts for the following
equation 5x – 8y = 40. Then graph.
35. Nancy and Jaime wanted buy their parents gifts for
Christmas which was 2 months away. They both
worked at Carl’s Jr. earning minimum wage.
Nancy figured she could save $12 a week and she
already had $52 in her piggy bank at home. Jaime
decided to work extra hours and save $26 a week.
Unfortunately he did have any money to start with.
Write equations and graph each situation.
y
6
Which had more money saved in 2 months (8
weeks)?
4
2
–6 –4 –2
–2
–4
–6
2
4
6
x
Estimate how long it would take for each of them to
have the same amount of money.
GEOMETRY
Answer Section
PRACTICE
Test 2
(3.5-3.6)
SHORT ANSWER
1. ANS:
–4
PTS: 1
DIF: L2
OBJ: 3-1.2 Properties of Parallel Lines
TOP: 3-1 Example 5
2. ANS:
83
REF: 3-1 Properties of Parallel Lines
STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0
KEY: corresponding angles | parallel lines |
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: angle | triangle | exterior angle | Polygon Angle-Sum Theorem
3. ANS:
73
PTS: 1
DIF: L3
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: pentagon | exterior angle | sum of angles of a polygon
4. ANS:
114
PTS: 1
DIF: L3
OBJ: 3-5.2 Polygon Angle Sums
KEY: hexagon | angle | exterior angle
5. ANS:
5 sides
REF: 3-5 The Polygon Angle-Sum Theorems
STA: CA GEOM 12.0| CA GEOM 13.0
PTS: 1
DIF: L2
OBJ: 3-5.2 Polygon Angle Sums
TOP: 3-5 Example 3
6. ANS:
x = 109, y = 60
REF: 3-5 The Polygon Angle-Sum Theorems
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: sum of angles of a polygon
PTS: 1
DIF: L2
OBJ: 3-5.2 Polygon Angle Sums
TOP: 3-5 Example 4
7. ANS:
72°
REF: 3-5 The Polygon Angle-Sum Theorems
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: exterior angle | Polygon Angle-Sum Theorem
PTS: 1
DIF: L2
OBJ: 3-5.2 Polygon Angle Sums
TOP: 3-5 Example 5
8. ANS:
m (interior) = 120
m (exterior) = 60
REF: 3-5 The Polygon Angle-Sum Theorems
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: angle | pentagon | Polygon Angle-Sum Theorem
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: Polygon Exterior Angle-Sum Theorem | exterior angle | interior angle
9. ANS:
y = –3x – 3
y
6
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
OBJ: 3-6.1 Graphing Lines
TOP: 3-6 Example 3
KEY: slope-intercept form | point-slope form | graphing
10. ANS:
a. Vertical angles.
b. Transitive Property.
c. Alternate Interior Angles Converse.
PTS:
OBJ:
TOP:
KEY:
11. ANS:
1
DIF: L2
REF: 3-2 Proving Lines Parallel
3-2.1 Using a Transversal
STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0
3-2 Example 1
two-column proof | proof | reasoning | corresponding angles | multi-part question
PTS: 1
DIF: L3
REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem
OBJ: 3-4.2 Using Exterior Angles of Triangles
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: Triangle Angle-Sum Theorem | exterior angle
12. ANS:
Standard form. Answer may vary. Sample: You could use the given form. Find the intercepts and use them to draw
the line.
PTS: 1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
OBJ: 3-6.2 Writing Equations of Lines
KEY: graphing | point-slope form | standard form of a linear equation | slope-intercept form | writing in math
OTHER
13. ANS:
A polygon is convex if the points of all the diagonals are inside or on the polygon.
PTS: 1
DIF: L3
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.1 Classifying Polygons
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: classifying polygons | concave | convex | writing in math
14. ANS:
D; a polygon is convex, not concave, if no diagonal contains point outsides the polygon.
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: polygon | writing in math | reasoning | interior angle | Polygon Angle-Sum Theorem
ESSAY
15. ANS:
[4]
[3]
[2]
[1]
correct idea, some details inaccurate
correct idea, some statements missing
correct idea, several steps omitted
PTS: 1
DIF: L4
REF: 3-2 Proving Lines Parallel
OBJ: 3-2.1 Using a Transversal
STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0
KEY: two-column proof | proof | extended response | rubric-based question | parallel lines | supplementary angles
16. ANS:
[4] a.
180(n – 2)
b.
c.
d.
360
e.
[3]
[2]
[1]
This makes sense because an interior angle and its
adjacent exterior angle are supplementary.
parts a–d correct; small error in part e
parts a–d correct
three correct answers
PTS: 1
DIF: L4
REF: 3-5 The Polygon Angle-Sum Theorems
OBJ: 3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
KEY: exterior angle | Polygon Exterior Angle-Sum Theorem | extended response | rubric-based question
MULTIPLE CHOICE
17. ANS:
OBJ:
KEY:
18. ANS:
OBJ:
KEY:
19. ANS:
OBJ:
B
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
Polygon Exterior Angle-Sum Theorem
C
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.1 Graphing Lines
TOP: 3-6 Example 2
graphing | standard form of a linear equation
D
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
KEY:
20. ANS:
OBJ:
KEY:
21. ANS:
OBJ:
KEY:
22. ANS:
OBJ:
23. ANS:
OBJ:
KEY:
24. ANS:
OBJ:
25. ANS:
OBJ:
26. ANS:
OBJ:
27. ANS:
OBJ:
KEY:
28. ANS:
OBJ:
TOP:
KEY:
29. ANS:
OBJ:
TOP:
30. ANS:
OBJ:
KEY:
31. ANS:
OBJ:
KEY:
32. ANS:
OBJ:
KEY:
33. ANS:
OBJ:
34.
35.
Polygon Angle-Sum Theorem
B
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
polygon | classifying polygons | equilateral
B
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
polygon | classifying polygons | equilateral
C
PTS: 1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
KEY: slope-intercept form
B
PTS: 1
DIF: L2
REF: 3-5 The Polygon Angle-Sum Theorems
3-5.2 Polygon Angle Sums
STA: CA GEOM 12.0| CA GEOM 13.0
polygon | classifying polygons | equilateral
B
PTS: 1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
KEY: word problem | problem solving | slope-intercept form
D
PTS: 1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
KEY: slope-intercept form | slope
D
PTS: 1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
KEY: graphing | slope-intercept form | slope | y-intercept
D
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
TOP: 3-6 Example 5
point-slope form
A
PTS: 1
DIF: L2
REF: 3-1 Properties of Parallel Lines
3-1.2 Properties of Parallel Lines
STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0
3-1 Example 3
proof | two-column proof | supplementary angles | parallel lines | reasoning
A
PTS: 1
DIF: L3
REF: 3-2 Proving Lines Parallel
3-2.1 Using a Transversal
STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0
3-2 Example 1
KEY: parallel lines | reasoning | supplementary angles
A
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.1 Graphing Lines
TOP: 3-6 Example 1
slope-intercept form | graphing
D
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
TOP: 3-6 Example 4
point-slope form
C
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
TOP: 3-6 Example 6
vertical line
D
PTS: 1
DIF: L2
REF: 3-6 Lines in the Coordinate Plane
3-6.1 Graphing Lines
TOP: 3-6 Example 2