Download Geometry Model Problems Test (California Essential Standards)

Geometry Model Problems Test (California Essential Standards)
GE 1.0
1. Which of the following is a list of the undefined terms in Geometry:
a. Point, line, plane.
b. Ray, line, line segment.
c. Point, line, line segment.
d. Ray, line segment, plane.
2. While working with drawings of quadrilaterals, Deanna made the following observation:
Opposite angles of parallelograms are congruent.
Although she had not proven the statement was true, she planned to ask her class to prove that it was.
Deanna’s observation would be best described by which term below?
a. A theorem.
b. An axiom.
c. An undefined term.
d. A conjecture.
GE 2.0
3. Theorem: A triangle has at most one obtuse angle.
Eduardo is proving the theorem above by contradiction. He began by assuming that in ABC, ∠A and ∠B
are both obtuse. Which theorem will Eduardo use to reach a contradiction?
a. If two angles of a triangle are equal, the sides opposite the angles are equal.
b. If two supplementary angles are equal, the angles measure 90 ˚.
c. The largest angle in a triangle is opposite the longest side.
d. The sum of the measures of the angles of a triangle is 180 ˚.
4. Use the proof to answer the
question below.
Given: AB ≅ BC ; D is the midpoint of AC
Prove:
STATEMENT
1. AB ≅ BC ; D is the midpoint 1. Given
REASON
of AC
2. AD ≅ CD
2. Definition of midpoint
3. BD ≅ BD
4.
3. Reflexive Property
4. ?
What reason can be used to prove that the triangles are congruent?
a.
b.
c.
d.
AAS
ASA
SAS
SSS
5.
Given: ∠2 ≅ ∠3
Prove: ∠1 ≅ ∠4
Use the proof to answer the question below.
STATEMENT
1. ∠2 ≅ ∠3
2. ∠1 ≅ ∠2; ∠3 ≅ ∠4
3. ∠1 ≅ ∠4
REASON
1. Given
2. ?
3. Transitive Property
What reason can be used to justify step 2?
a. Vertical angles are congruent.
b. Complements of congruent angles are congruent.
c. Supplements of congruent angles are congruent.
d. Corresponding angles are congruent.
GE 3.0
6. GRAM is a parallelogram. If GR = RA, which of the following must also be true?
a. GRAM is a square
b. GA = RM
c. GRAM is a rectangle
d. GRAM is a rhombus
7. LATR is a parallelogram. If ∠L ≅ ∠A, and m∠L + m∠A = 180˚, which of the following must also be
true?
a. LATR is a square
b. LATR is a rhombus
c. LATR is a rectangle
d. LT ⊥ AR
8.
All rectangles are squares.
Which of the following diagrams is a counterexample to the statement?
a.
c.
b.
d.
9.
If two triangles have two pairs of angles congruent and one pair of sides
congruent , then the two triangles are congruent.
Which of the following diagrams is a counterexample to the statement?
a.
d.
c.
b.
GE 7.0
10. In the diagram, lines l and m are cut by a transversal. If
which of the following could be used to prove that are parallel?
a. Converse of the Alternate Interior Angles Theorem.
b. Converse of the Alternate Exterior Angles Theorem.
c. Converse of the Corresponding Angles Postulate.
d. Converse of the Consecutive Interior Angles Theorem.
,
11. Lines l and m are shown in each diagram. In which diagram MUST lines l and m be parallel?
a.
b.
c.
12. For the quadrilateral shown, what is the value
of x?
a. 8
b. 16
c. 18
d. 20
13. In the diagram, quadrilateral TRAP is a
trapezoid in which
. What is the value of x?
a. 12.5
b. 8
c. 5
d. 4
14. In the diagram shown, what is the value of x?
a. 10
b. 16
c. 18
d. 24
d.
15. Quadrilateral ABCD is circumscribed by a circle, as shown in the
diagram to the right. What is the measure of C?
a. 70°
b. 82°
c. 86°
d. 94°
GE 4.0
16. If
and
and
have sides
sufficient to prove that
, which of the following would be
?
a.
b.
c.
d.
17. Which two must be similar?
a. Two isosceles right triangles
b. Two isosceles trapezoids
c. Two rhombi
d. Two rectangles
18. Which triangles must be similar?
a.
b.
c.
d.
19. In quadrilateral QUAD, QU is parallel to DA . If QD is not congruent to UA , then which
statement below must also be true?
a.
b.
c. QUAD is a parallelogram.
d. QUAD is a trapezoid.
GS 17.0
20. In the diagram, ABCO is a parallelogram.
What are the coordinates of the intersection of the
diagonals?
c

 a, b + 
2

a

b.  , b + c 
2

 b+c 
c.  a ,

2 

a b+c 
d.  ,

2 2 
a.
GE 5.0
21.
Given: ABCD is a rhombus
Which theorem or postulate listed below could
be used to prove that
?
a.
b.
c.
d.
and AC bisects DB .
Prove:
22. In the diagram below, ∠A ≅ ∠D and
∠B ≅ ∠E .
AAA
SSA
AAS
SSS
What additional information would be enough to
prove that
?
a.
b.
c.
d.
GE 6.0
23. If two sides of a triangle are 6 inches and 10 inches, what is the smallest whole number length that could be
the third side?
a. 16 inches.
b. 15 inches.
c. 5 inches.
d. 4 inches.
GE 17.0
24. In the diagram, ABCO is a parallelogram.
What are the coordinates of the intersection of
the diagonals?
a.
b.
c.
d.
25. In the diagram, ABC is a right triangle.
What is the slope of BC ?
a.
c.
b.
d.
31.
What is the sum of the measures of ∠a and ∠b?
a.
b.
c.
d.
GE 13.0
33.
102°
152°
176°
184°
In the diagram shown m∠ACB =111˚. What is the measure
of ∠CBA ?
a.
b.
c.
d.
48°
42°
27°
21°
34.
In the diagram shown, what is the measure of the angle
marked X?
a. 114˚
b. 145˚
c. 156˚
d. 160˚
GE 22.0
35.
If ABC is rotated 90˚clockwise about the origin to
form A’B’C’, what would be the coordinates of
A’?
a. A’ (-3, -1)
b. A’ (-1, -3)
c. A’ (1, 3)
d. A’ (3, 1)
36. The coordinates of the vertices of
units down and 4 units to the right to create
?
a.
b.
c.
d.
37.
,
,
,
,
, are
,
,
. If
is translated 2
, what are the coordinates of the vertices of
,
,
,
,
If quadrilateral DEFG is reflected across the y-axis, it
would create quadrilateral D’E’F’G’. What are the
coordinates of point G’ ?
a. G’ (6, 2)
b. G’ (-6, -2)
c. G’ (-2, -6)
d. G’ (2, 6)
GE 14.0
38.
A diagram from a proof of the Pythagorean Theorem
is shown. Which expression could be used to
complete the expression by representing the areas
of the smaller objects on the right side of this
equation :
?
a.
b.
c.
d.
GE 15.0
a. 5
39. A right triangle’s hypotenuse has length 11. If one leg has
length 6, what is the length of the other leg?
40.
b.
85
c. 157
d. 17
In a basketball game, a player from the home team threw the ball from
corner C to a player standing at point E. (E is the midpoint of AD ). Then
the player at point E threw the ball to a player at corner B. If the court
was 80 feet long and 50 feet wide, how far was the ball thrown? (Leave in
simplified radical form)
a. 10 41 feet
b. 20 41 feet
c. 10 89 feet
d. 20 89 feet
GE 18.0
41.
In the figure shown,
,
, and
. What is the approximate length of BC ?
a.
b.
c.
d.
42.
4 in.
16 in.
20 in.
36 in.
In the figure below, if tan A =
4
, what are
3
and
?
a.=
sin A
4
3
=
,cos A
7
7
b.
=
sin A
3
4
=
,cos A
7
7
c.
=
sin A
3
4
=
,cos A
5
5
d.=
sin A
4
3
=
,cos A
5
5
43.
A ladder is leaned against a wall at an
angle of 65° to the ground. How far off
the ground does the ladder touch the wall?
a.
b.
c.
d.
12 feet
27 feet
33 feet
63 feet
GE 19.0
Triangle JKL is shown in the diagram. Which
equation should be used to find the length
44.
of LJ ?
a.
b.
c.
d.
45.
On a swing set, on engineer used a
support bar that was 20 feet long. If
the support bar forms a 70° angle to
the ground, how far apart will the
support bars be at the base?
a.
b.
c.
d.
46.
18.8 feet
13.6 feet
37.6 feet
55 feet
In the diagram,
and
equation could be used to find BC?
a.
b.
c.
d.
. Which
GE 20.0
47.
The right triangle in the diagram has one side with a length of
What is the length of the side marked ?
.
a. 5
b. 15
c.
d.
GE 21.0
48.
 = 60 , and the
In the circle shown, the measure of BC
?
measure of ∠BAD =
62 . What is the measure of CD
a.
b.
c.
d.
49.
60˚
62˚
64˚
68˚
In the circle shown, DF and CE are chords
intersecting at G. If DG = 9, FG = 4, and EG = 12, what is
the length of CG ?
50.
a. 3
b. 3.4
c. 5.3
d. 7
In the circle shown, what is the measure of angle 1?
a.
b.
c.
d.
51.
14˚
28˚
33˚
71˚

LM is tangent to a circle, whose center is C, at point M.
MQ is a diameter. If m∠QNP = 65˚ and m∠NPM = 50˚,
what is m∠PMR?
a.
b.
c.
d.
52.
A square is circumscribed about a circle. What is the ratio of the
circumference of the circle to the perimeter of the square?
a.
GE 8.0
53.
40˚
50˚
65˚
75˚
b.
c.
d.
A cylinder rolls across a table top for 10 complete revolutions. If the
diameter of the base is 6 inches, how far did the cylinder travel? (Leave
the answer in terms of π).
X
a. 60π in.
54.
b. 90π in.
c. 120π in.
d. 360π in.
The prism shown has a base in the shape of a right triangle. What is the
lateral surface area of the prism?
a.
b.
c.
d.
55.
36 square centimeters
66 square centimeters
72 square centimeters
84 square centimeters
What is the volume of the prism shown?
a.
b.
c.
d.
56.
350 cubic millimeters
286 cubic millimeters
280 cubic millimeters
230 cubic millimeters
A target for a yard game is made with areas that are alternately
painted white and gray, as shown in the diagram. The inner circle is
white and has a radius of 1 inch. Each of the other three rings has a
radius 1 inch more than the ring before it. What is the area of the
white portion of the target?
a.
b.
c.
d.
5π square inches
6π square inches
8π square inches
10π square inches
GE 10.0
57.
A rectangle that is 12 feet wide has a perimeter of 40 feet. What is the area of the rectangle?
a.
b.
c.
d.
96 square feet
192 square feet
240 square feet
480 square feet
58.
Each side of a triangle measures 4 m. What is the area of the triangle?
(Leave the answer in simplified radical form).
a. 12 square meters
square meters
b.
c. 4 square meters
square meters
d.
59.
Quadrilateral ABCD is a rhombus. If BC = 5 inches and BD = 6
inches, what is the area of ABCD?
a.
b.
c.
d.
60.
The diagram shows a trapezoid with a height of 4 cm.
What is the area of the trapezoid?
a.
b.
c.
d.
GE 11.0
61.
15 square inches
24 square inches
30 square inches
48 square inches
22 square centimeters
24 square centimeters
32 square centimeters
42 square centimeters
The volume of a right rectangular prism is calculated to be 18 cubic centimeters. If the length, the
width, and the height of the prism are all doubled, what would be the volume of the new prism?
a.
b.
c.
d.
GE 9.0
62.
The cylinder shown has a height of 4 cm and the diameter
of the base is 10 cm. What is the volume of the cylinder?
a.
b.
c.
d.
63.
26 cubic centimeters
36 cubic centimeters
72 cubic centimeters
144 cubic centimeters
400π cubic centimeters
100π cubic centimeters
80π cubic centimeters
40π cubic centimeters
The pyramid shown has a square base that measures 8 cm
on each side. The slant height of the pyramid is 6 cm.
What is the surface area of the prism?
a.
b.
c.
d.
128 square centimeters
160 square centimeters
256 square centimeters
288 square centimeters
GE 16.0
64. Given:
. What is the first step in constructing the perpendicular
bisector to ?
a.
b.
c.
d.
65.
66.
Draw a line segment connecting points E and F.
From point C, draw an arc that intersects the line at points A and B.
Draw a line segment connecting points A and B.
From points A and B, draw equal arcs that intersect at points E and F.
Darla is constructing an equilateral triangle. Which of the following could be her first step?
a.
c.
b.
d.
Marsha is using a straightedge
and compass to do the
construction shown.
Which statement best describes the construction Martha is
doing?
a. a line through P parallel to line l by constructing two
lines perpendicular to the same line
b. a line through P parallel to line l by copying an angle
c. a line through P perpendicular to line l
d. a line through P congruent to line l
67.
Amina is bisecting an angle. Which of the construction diagrams shown below best represents the
beginning of Amina’s construction?
c.
a.
b.
d.