Download Key - Coach Shue`s Teacher Page

4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
Analytic Geometry (CCGPS) EOCT Quiz Answer Key
Geometry - (MCC9‐12.G.CO.6 ) Rigid Motions, (MCC9‐12.G.CO.7 ) Congruence & Rigid Motions, (MCC9‐12.G.CO.8 ) Criteria For
Triangle Congruence, (MCC9‐12.G.CO.9 ) Line And Angle Theorems, (MCC9‐12.G.CO.10 ) Triangle Theorems, (MCC9‐12.G.CO.11 )
Parallelogram Theorems, (MCC9‐12.G.CO.12 ) Formal Geometric Constructions, (MCC9‐12.G.SRT.1 ) Properties Of Dilations, (MCC9‐
12.G.SRT.2 ) Similarity And Transformations, (MCC9‐12.G.SRT.3 ) AA Criterion And Similarity
Student Name:
_______________________
Teacher Name: Micah Shue
_________
Score: _________
Date:
1)
Describe the transformation.
A)
reflection across the x-axis
B)
reflection across the y-axis
C)
ref l ection across th e l in e y = x
D)
reflection across the line y = -x
Expl an ation :
The transformation is a Ref l ection across th e l in e y = x. If the graph was folded along the line y = x, the points of the two
triangles would correspond to each other.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
1/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
2)
Which reason explains the congruency of these two triangles?
A)
AAA
B)
HL
C)
SAS
D)
SSS
Expl an ation :
HL. Based on the markings in the diagrams, you can see that the hypotenuse and leg of one triangle are congruent to the
hypotenuse and leg of the second triangle.
3)
Which of the statements about the two triangles is correct?
A)
The triangles are congruent by AAA.
B)
T h ese trian gl es are con gruen t by AAS.
C)
These triangles are congruent by SSS.
D)
These triangles are congruent by SSA.
Expl an ation :
The solution is T h ese trian gl es are con gruen t by AAS. The given information is an Angle-Angle-Side, this is enough to prove
that these triangles are congruent.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
2/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
4)
ΔSAM≅ΔRAT
Which statement is not necessarily true?
A)
MA = TA
B)
MS = TR
C)
∠ M≅ ∠ R
D)
∠M≅∠T
Expl an ation :
Solution: ∠ M≅ ∠ R. According to the congruence statement, we do not know that ∠M≅∠R.
5)
Which theorem proves that the triangles are congruent?
A)
ASA
B)
SAS
C)
SSA
D)
SSS
Expl an ation :
The solution is SAS. Since vertical angles are congruent, we can say that the triangles are congruent by SAS.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
3/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
6)
Fill in the missing reason in the proof.
A)
ASA
B)
SAA
C)
SAS
D)
SSS
Expl an ation :
The correct answer is SAS. Throughout the course of the proof you show that two legs and the angle between them are congruent.
7)
Given that j || k, what is the measure of the missing angle?
A)
30°
B)
40°
C)
60°
D)
120°
Expl an ation :
The solution is 6 0 °. Since the angles are on the same side of the transversal, and outside of the two parallel lines, we can conclude
that the angles are supplementary. These are sometimes called "same-side exterior angles".
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
4/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
8)
If angle A in the diagram equals 45 degrees and angle B is 4x + 5 degrees, determine the value of x.
A)
1 0 degrees
B)
25
degrees
2
C)
D)
40 degrees
160 degrees
Expl an ation :
The correct value of x is 1 0 degrees. Since the angles are vertical angles we know that their measurements are equal, so set the
two measurements equal to each other and solve.
9)
∠a are ∠e are ______ angles.
A)
perpendicular
B)
correspon din g
C)
complementary
D)
alternate interior
Expl an ation :
C orrespon din g angles are formed when two parallel lines are intersected by a third line and they have equal measure.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
5/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
10)
Giv en : l in e a is paral l el to l in e b
Identify a pair of congruent alternate interior angles.
A)
3 & 6
B)
1&8
C)
2&5
D)
4&8
Expl an ation :
Angles 3 & 6 are congruent alternate interior angles. These angles line between the two lines on opposite sides of the transversal.
11)
Angles b and c are called ____________ angles.
A)
complementary
B)
linear
C)
supplementary
D)
v ertical
Expl an ation :
Solution: v ertical . We know that vertical angles are opposite angles formed by intersecting lines.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
6/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
12)
The three medians of ΔABC intersect at point E. Point E is the
A)
cen troid.
B)
circumcenter.
C)
incenter.
D)
orthocenter.
Expl an ation :
The solution is cen troid. The centroid of a triangle is the point of concurrency of the medians of a triangle. This point always lies
inside the triangle. It is the center of gravity for the triangle.
13)
If m∠A = 87° and m∠B = 32°, find m∠1.
A)
29°
B)
61°
C)
83°
D)
119°
Expl an ation :
1 1 9 ° is correct. Since A + B = 119, we know that C = 180 - 119 = 61°, and C is supplementary to angle 1.
1 4 ) The angles of a triangle are 2x, 3x, and 4x degrees. Find the value of x.
A)
20
B)
30
C)
40
D)
50
Expl an ation :
2 0 . The three angles of the triangle add up to 180 degrees. So, 2x + 3x +4x = 9x = 180, so x = 20.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
7/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
15)
A section of a roller coaster track forms a parallelogram ABCD.
If m∠ABC = 72°, what is m∠DAB?
A)
72°
B)
108°
C)
144°
D)
216°
Expl an ation :
108°
The opposite angles of any parallelogram are equal.
m∠ABC = m∠CDA = 72° and m∠DAB = m∠BCD
The sum of the angles of a parallelogram is 360°. This gives the equation m∠DAB + 72° + m∠BCD + 72° = 360°
2m∠DAB + 144° = 360°
m∠DAB° =
360° - 144°
2
= 108°
1 6 ) The diagonals of a _________________ are ALWAYS congruent.
A)
parallelogram
B)
rectan gl e
C)
rhombus
D)
trapezoid
Expl an ation :
rectan gl e. The diagonals of a rectangle are always congruent.
1 7 ) In which quadrilateral are the diagonals perpendicular?
A)
parallelogram
B)
rectangle
C)
rh om bus
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
8/16
4/23/2014
D)
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
trapezoid
Expl an ation :
The solution is rh om bus. One of the special properties of a rhombus is the fact that it has perpendicular diagonals.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
9/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
1 8 ) A rhombus is NOT a _____________ .
A)
parallelogram
B)
polygon
C)
quadrilateral
D)
trapezoid
Expl an ation :
A rhombus is not a trapezoid. A trapezoid is a quadrilateral with exactly 2 parallel sides.
19)
In parallelogram ABCD, find m∠A.
A)
15°
B)
70°
C)
110°
D)
200°
Expl an ation :
The sum of consecutive angles of a parallelogram is 180°. So, 6x + 20 + 4x + 10 = 180, and x = 15. Since we are looking for m∠A, we
plug 15 into 6x + 20 and get 110. The correct answer is 1 1 0 °.
2 0 ) On a map of Alabama, one inch is equivalent to 100 miles. If the distance between two towns is 0.5 inches on the map, what is
the actual distance between the towns?
A)
5 0 m il es
B)
100 miles
C)
200 miles
D)
1000 miles
Expl an ation :
If each inch = 100 mile and there is 0.5 inches between the towns, then the total number of miles = 100miles/inch x 0.5 inches =
5 0 miles.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
10/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
21)
Given: ∠1 ≅ ∠8
Which lines must be parallel?
A)
r and s
B)
p an d q
C)
p and r
D)
q and s
Expl an ation :
The solution is p an d q. Since angles 1 and 8 are congruent alternate exterior angles and r is the transversal, we can conclude that
lines p and q are parallel.
22)
Determine which statement is true.
A)
t ll u and v ll w
B)
t ll w and u ll v
C)
t l l v an d u l l w
D)
t ll u and u ll v
Expl an ation :
The solution is t l l v an d u l l w . Since 60° and 120° are supplementary, this allows us to conclude that lines t and v are parallel.
Also, since 70° and 110° are supplementary we can conclude that lines u and w are parallel.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
11/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
23)
If ΔABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point B'?
A)
(0, 0)
B)
(0, 3)
C)
(0 , 6 )
D)
(0, 12)
Expl an ation :
The solution is (0 , 6 ). In the new triangle the side that corresponds to AB will be 6 units. Since the center is (0, 0), point B' will fall
at point (0, 6).
24)
If ΔABC is dilated by a scale factor of
A)
B)
C)
D)
1
2
with a dilation center of A, what will be the coordinates of point C'?
(0, 0)
(1 , 0 )
(0, 1)
(4, 0)
Expl an ation :
The solution is (1 , 0 ). In the new triangle the side that corresponds to AC will be 1 unit. Since the center is (0, 0), point C' will fall at
point (1, 0).
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
12/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
25)
Solve for BC.
A)
12
B)
10
C)
8
D)
6
Expl an ation :
Solution: 1 2 . To solve for BC, use the proportion 4/6=x/18, 6x = 72, x = 12.
26)
The quadrilaterals are similar.
If CB = 6, GF = 3, and CD = 4, find GH.
A)
2
B)
3
C)
8
D)
10
Expl an ation :
The solution is 2 . The side lengths in ABCD are twice as long as the side lengths in EFGH.
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
13/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
27)
ΔEFG ~ ΔLMN. Find LN.
A)
2.5
B)
3
C)
3.5
D)
5
Expl an ation :
The solution is 3 . 5 . The problem can be solved using the proportion:
2 7
=
1 x
28)
If ΔABC is similar to ΔDEF, the m∠A = 50°, and m∠E = 70°, what is m∠C?
A)
60°
B)
70°
C)
90°
D)
120°
Expl an ation :
6 0 ° is the correct answer.
Since ΔABC is similar to ΔDEF, the m∠E = m∠B = 70°.
We're given that m∠A = 50°.
The sum of the angles in a triangle is 180°,
so m∠C = 180 - 70 - 50 = 60°
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
14/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
29)
Given the picture, solve for x.
A)
8
B)
9
C)
15
D)
17
Expl an ation :
1 5 is the correct answer.
ΔTriangle BCD ∼ Δ ACE, so corresponding sides are proportional.
CD = 4 and CE = (4 + 6) = 10
BD = 6 and AE = x
Let's set up a proportion:
x 10
=
6
4
10
x = 6( )
4
x = 15
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
15/16
4/23/2014
USATestprep, Inc. - Online State-Specific Review and Benchmark Testing
30)
If ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?
A)
y es, by AA criterion
B)
yes, by SAS criterion
C)
yes, by SSA criterion
D)
no, not possible to tell.
Expl an ation :
If two angles in a triangle are congruent to two angles in another triangle then the two triangles are congruent. ∠BAC ≈ ∠CED since
they have the same measure. ∠ACB ≈ ∠DCE since they are vertical angles. Since two angles are congruent, then you can conclude
y es, by AA criterion
http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=536
16/16