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Geometry SLO #2 Pretest
ABC are A ÊÁË 2,5 ˆ˜¯ , B ÊÁË 1,−4 ˆ˜¯ , and C ÊÁË −3,−1 ˆ˜¯ .
What are the coordinates of the image after the translation ÊÁË x,y ˆ˜¯ → ÊÁË x + 2,y − 5 ˆ˜¯ ?
1. The vertices of
A′ ÊÁË 7,−3 ˆ˜¯ , B ′ ÊÁË 6,−6 ˆ˜¯ , and C ′ ÊÁË 2,−3 ˆ˜¯
b. A′ ÊÁË 0,10 ˆ˜¯ , B ′ ÊÁË −1,1 ˆ˜¯ , and C ′ ÊÁË −5,4 ˆ˜¯
c. A′ ÊÁË 4,0 ˆ˜¯ , B ′ ÊÁË 3,−9 ˆ˜¯ , and C ′ ÊÁË −1,−6 ˆ˜¯
d. A′ ÊÁË 4,10 ˆ˜¯ , B ′ ÊÁË 3,1 ˆ˜¯ , and C ′ ÊÁË −1,4 ˆ˜¯
a.
2. What is the reason for step #5?
Given: GJ bisects ∠FGH , FG ≅ HG
Prove: FJ ≅ HJ
Proof:
Statements
1. GJ bisects ∠FGH
2. ∠FGJ ≅ ∠HGJ
3. FG ≅ HG
4. ∠F ≅ ∠H
5. FGJ ≅ HGJ
6. FJ ≅ HJ
a.
b.
c.
d.
Reasons
1. Given
2. Definition of Angle Bisector
3. Given
4. Isosceles Triangle Theorem
5.
?
6. CPCTC
SSS
HL
ASA
AAS
1
°
°
5. Which statement would NOT prove that ABCD is a
parallelogram?
3. If m∠3 = (4x + 20) and m∠5 = (6x + 10) , what
value of x proves that r Ä s?
a.
b.
c.
d.
5
15
40
100
a.
b.
AC ≅ CD and AB ≅ BD
AB Ä CD and AB ≅ CD
c.
d.
∠A ≅ ∠D and ∠B ≅ ∠C
AD and CB bisect each other
6. Name three points that are collinear.
4. In
a.
b.
c.
d.
DEFG, solve for the length of EG.
a.
b.
c.
d.
10
25
30
50
2
G, H, and I
G, H, and J
G, F, and I
G, J, and I
7. Which angles are adjacent but do NOT form a
linear pair?
10. Which of the following diagrams represents a
rotation about Q, then a translation parallel to line
l?
a.
a.
b.
c.
d.
∠1 and ∠5
∠2 and ∠3
∠2 and ∠4
∠4 and ∠5
b.
8. The preimage for a reflection is shaded. Which
represents the mapping?
c.
a. ABCD → HEFG
b. GHEF → ADCB
c. BCDA → FEHG
d. DABC → FGHE
d.
9. What are the coordinates of the image of ÊÁË −3,2 ˆ˜¯
when the point is reflected across the line y = 4?
a.
b.
c.
d.
ÁÊ −3,4 ˜ˆ
Ë
¯
ÁÊ −1,6 ˜ˆ
Ë
¯
ÁÊ 6,−3 ˜ˆ
Ë
¯
ÁÊ −3,6 ˜ˆ
Ë
¯
3
11. Which two triangles are similar?
a.
ABC ∼ DEF
b.
ABC ∼ GHJ
c.
DEF ∼ GHJ
d. can not determine
12. Complete the similarity statement.
ABC ∼
a.
b.
c.
d.
13.
__________
°
KLM ≅ RST . m∠L = (3x + 15) and the
°
m∠S = (6x + 3) . What is the value of x?
a.
b.
c.
d.
ZYX
YZX
XZY
XYZ
4
2
4
6
27
14. If
a.
PQR ∼
3
16. Which angle has a cosine of ?
5
FGH , solve for the measure of QR.
3
2
b. 1
c. 2
d. 3
a.
b.
c.
d.
15. Shadows were measured at the same time of day to
determine the height of a grain silo. If the silo’s
shadow measure 15 ft and the height of the silo is
60 ft, which measurements were used to find the
height?
a.
b.
c.
d.
∠A
∠B
∠C
none of the above
17. Which is approximately equal to the sine of ∠A?
2-meter pole with a 5-meter shadow
5-foot person with a 15-inch shadow
10-foot pole with a 40-foot shadow
2-meter person with a 3-meter shadow
a.
b.
c.
d.
5
0.55
0.63
0.86
1.58
18. An air traffic controller at an airport sights a plane
at an angle of elevation of 34 ° . The pilot reports
that the plane’s altitude is 3200 ft. To the nearest
foot, what is the horizontal distance between the
plane and the airport?
a.
b.
c.
d.
20. A utility worker is installing a 25-foot telephone
pole. The work order indicates that two guy wires
(a wire running from the ground to the top of the
pole) should be placed opposite each other and at a
65 ° angle of elevation to the pole. To the nearest
tenth of a foot, how far apart are the guy wires?
a.
b.
c.
d.
4744 ft
2159 ft
3200 ft
5723 ft
21. Which of the following is the equation of a line
that passes through ÁÊË 2,1 ˜ˆ¯ and is perpendicular to
the line passing through the points ÁÊË −4,1 ˜ˆ¯ and
ÊÁ 3, −2 ˆ˜ ?
Ë
¯
19. A forest ranger in 140-foot observation tower sees
a fire moving in a direct path towards a lake. The
angle of depression to the lake is 8 ° , and the angle
of depression to the fire is 3 ° . To the nearest foot,
how close is the fire to the base of the observation
tower? (The figure is not drawn to scale.)
a.
b.
c.
d.
11.7 ft
23.3 ft
27.6 ft
not here
997 ft
1675 ft
2671 ft
not here
6
7
11
3
a.
y = 3 x+
b.
y = −7 x −
c.
y = 7 x+
3
11
3
d.
y = 3 x−
7
11
3
3
11
3
22. Which of the following is the equation of a line
that passes through ÊÁË 4,1 ˆ˜¯ and is parallel to
25. What is the area of the polygon with the vertices
W ÊÁË −4,2 ˆ˜¯ , X ÊÁË 1,2 ˆ˜¯ , Y ÊÁË 1,−2 ˆ˜¯ , and Z ÊÁË −4,−2 ˆ˜¯ ?
6x − 3y = 21?
a.
b.
c.
d.
y = 2x − 7
y = 0.5x − 1
y = −0.5x + 3
y = −2x + 9
a.
b.
c.
d.
23. Describe the lines passing through the given points.
Line 1: ÊÁË 5,8 ˜ˆ¯ and ÁÊË 4,3 ˜ˆ¯
Line 2: ÁÊË −4,9 ˜ˆ¯ and ÁÊË −2,−1 ˜ˆ¯
a.
b.
c.
d.
parallel
perpendicular
horizontal
none of the above
24. What is the perimeter of square DEFG if the
coordinates of D and E are D ÁÊË 0,0 ˜ˆ¯ and E ÁÊË 0,3 ˜ˆ¯ ?
a.
b.
c.
d.
9 units 2
9 units
12 units 2
12 units
7
18 units 2
18 units
20 units 2
20 units
ID: A
Geometry SLO #2 Pretest
Answer Section
1. C
G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure
using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
2. C
G-CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
3. A
G-CO.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
4. D
G-CO.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent diagonals.
5. A
G-CO.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent diagonals.
6. A
G-CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
7. B
G-CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
8. C
G-CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.
9. D
G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure
using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
1
ID: A
10. B
G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure
using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
11. B
G-SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to
decide if they are similar; explain using similarity transformations the meaning of similarity for triangles
as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of
sides.
12. A
G-SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to
decide if they are similar; explain using similarity transformations the meaning of similarity for triangles
as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of
sides.
13. C
G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
14. B
G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
15. C
G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
16. A
G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
17. C
G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
18. A
G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
19. C
G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
2
ID: A
20. B
G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
21. D
G-GPE.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a
given point).
22. A
G-GPE.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a
given point).
23. D
G-GPE.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a
given point).
24. D
G-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g.,
using the distance formula.
25. C
G-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g.,
using the distance formula.
3