Download 3 + - Geometry101

Geometry
Posttest Review
2017
1. The polygons below are similar.
What is the scale factor of the
2. A man who is 5ft 6ins
dilation and find the missing side
tall stands beside a tree
length.
14ft 3ins tall. If his image
is 8ft long, how long is the
shadow of the tree?
? = 16
Length of shadow
= 20.7 ft
3. Given that AB = 2x – 3, BC
4. Find the value of x
= 5/3x + 2, DE = 4y + 9 and
6x – 4
EF = 7y + 3.
Find the value of x and y.
5x – 2
15
12
x = -6
5. Given the point A(-1, 2) and
2x – 3
4y + 9
B(7, 14), find the coordinate of
the point P on the directed line
5x + 2
3
7y + 3
x = 15
segment AB that partition AB in
the ratio 1:3. P is (2, 3)
y=3
If the distance between Lake Dr. and
6.
Lake Dr.
Van Dusen Rd. is 652m along
Ashford Rd. and 786m along Cherry
Ln. If the distance between
Baltimore Ave
Baltimore Ave. and Van Dusen Rd.
along Ashford is 312m, what is the
Van Dusen Rd.
Ashford Rd.
Cherry Ln.
distance between Baltimore Ave.
and Van Dusen Rd. along Cherry Ln.?
Distance between Baltimore Ave and Ashford Rd
along Cherry Ln = 259m
7. Are the following triangles
8. William plotted the four
similar? If so, what is the
corners of his backyard on a
similarity statement?
coordinate plane. The four
B
corners were (2, 5), (6, 4), (6, 2)
P
and (2, 0). What is the exact
name of the shape of his
backyard?
350
A
550
C Q
R
Riangles are similar
Similarity statement is ΔABC ≅ ΔPRQ
Shape is a trapezoid
9. Which similarity statement
10. Which two triangles are similar?
below best describes the
A
B
C
D
relationship between the three
triangles in the figure below?
R
T
S
S
S
Q
R T
Q
T
Similarity statement is ΔSTQ ≅ ΔRTS ≅ ΔRSQ
Δ in B ≅ Δ in C
11. Determine whether the dilation
from A to B is an enlargement or a
reduction. Then find the scale factor
of the dilation
12. Find the exact length of the
missing side in the given
triangle
x = √29
Enlargement
k = 5/2
13. Find the value of x in the right 15. An equilateral triangle has an
triangle below
altitude of 9m. Determine the
length of a side of the triangle
x = 6.60
9m
x
14. Find the length of the
hypotenuse of a 450-450-900
triangle with a leg of 5 inches.
hypotenuse = 5√2
side =6√3
16. Express each trigonometric
19. What is the perimeter of
ratio as a fraction for angle θ, when
ΔABC?
c = 10 and b = 6
θ
Sin θ = 6/10 = 3/5
Cos θ = 8/10 = 4/5
Tan θ = 6/8 = 3/4
Perimeter =2√10 + √53 + √89
17. Simon was sitting on horizontal ground level with the base of the
Washington Monument in D.C. The angle formed by the ground and the
line segment from his position to the top of the building is 57.8°. Given
that the height of the Monument is 555 feet. Find her distance from the
Washington Monument to the nearest foot
Distance, x = 555 ft/tan 57.80
= 350 ft
555 feet
57.8°
x feet
18. Two students graphed lines on a coordinate plane. One of the
student’s line is represented by the equation y = 5x – 2. The other
student’s line is parallel to the first student’s line. Which of the
following could be an equation for second student’s line?
A. y + 5x = -2
B. y + 5x = 8
C. y – 5x = 6
D. 5y – x = 2
A. y + 5x = -2  y = -5x – 2
B. y + 5x = 8  y = -5x + 8
C. y – 5x = 6  y = 5x + 6
D. 5y – x = 2  y = x/5 + 2
C. y – 5x = 6
20. Name the image of P under a
21. Which letter below has
rotation of 180° about point M
rotational symmetry?
H
22. Determine whether the figure
below has plane symmetry, axis
symmetry, both or neither
D
both
23. Draw the image below that
24. Name the plane not
represents the reflection of
intersecting plane BFGC in the
quadrilateral HLPQ over line m?
figure below.
H’
L’
Q’
P’
m
Plane AEHD
25. The logos for Mercedes Benz
and Volkswagen are shown below.
What type of congruence
transformation does each illustrate
Rotational
& Reflectional Reflectional
27. Which response below
shows a correct line of
symmetry in order to create a
reflection over the line?
26. Ray BD is an angle bisector of
∠ABC. If the m∠ABD = 5x – 2,
what is the m∠ABC?
m∠ABC = 10x - 4
28. What are the missing
29. LMJK is a quadrilateral, which
coordinates of this parallelogram? of the following statements are
not always true about LMJK if it is
a rhombus?
∠M ≅ ∠L;
C = (b, c)
JK ≅ ML; JM ≅ KL; ∠M ≅ ∠L; ∠JMK ≅ ∠LKM;
JK // ML; slope of JK = slope of ML;
MK bisects ∠M; ΔMJK ≅ ΔKLM.
30. Consider the given statement and conjecture below. Determine
whether the conjecture is true or false.
Give a counterexample if the conjecture is false.
Given: ∠M is complementary to ∠P and ∠P is complementary to ∠R.
5x – 3 = 12; x = 3
Conjecture: ∠M is complementary to ∠R.
2y + 3 = 12; y = 4.5
31. Lines ZC, AW, and BY are
4z – 3 = 9; z = 3
perpendicular bisectors of the
sides of ΔABC and meet at P.
If AP = 5x – 3, BP = 2y + 3, CP = 12,
AE = 4z – 3, find x, y, and z.
9
32. Determine whether the
33.
quadrilateral is a parallelogram.
If the quadrilateral is a
parallelogram, state the
justification.
∠MNP ≅ ∠NPO
Given
Reflexive property
SAS
Two pairs of opposite
angles and congruent
MP ≅ NO
34. If the slope of AB = 3/7 and the
m = 3/7
m = -5/6
slope of
BC = - 5/6, what is the slope of CD
so if ABCD is a parallelogram?
35. If ∠C ≅ ∠A and ZA//CB, which
theorem or postulate can be used
to prove ABDZ is a parallelogram?
)
SAS theorem
//
(
m = 3/7
slope of CD = 3/7
36. Is it possible to form a triangle
with side lengths 4, 10, 3? If not,
No, 4 + 3 < 10
explain why not.
37. Find the coordinates of the
intersection of the diagonals of
parallelogram WXYZ with vertices
W(-4, -4), X(-2, 1), Y(5, 2), Z(4, -3).
Since the diagonals bisect
each other, point of
intersection is the
midpoint.
MXZ = (4 + -2, -3 + -2)
2
2
= (1, - 1)
38. Find the values of w and z in
parallelogram below
4z – 5 = 2z + 1
z=3
4w = w + 3
w=1
39. Given A(4, 1), B(6, 3), and C(1, 3),
D(3, 5)
.
what is the coordinate of D, if AB
.
C(1, 3)
parallel to CD?
D(3, 5)
. B(6, 3)
. A(4, 1)