Download Geometry Spring Semester Exam Review 2015-2016

Geometry
Spring Semester
Exam Review
2015-2016
Name: ______________________
Chapter 12 - Due: __________
Chapter 11 - Due: __________
Chapter 10 - Due: __________
Chapter 8 - Due: __________
Chapter 7 - Due: __________
Chapter 6 - Due: __________
Name _________________________________
Geometry – Spring Semester Review (15-16)
Date ______________________
SEMESTER REVIEW: Chapter 12
SHOW ALL WORK!! Don’t forget your units! Leave answers in terms of π
1. Write the formulas for the following:
________________________area of a triangle
________________________area of a rectangle
________________________area of a circle
________________________area of a regular polygon
________________________area of a trapezoid
________________________circumference of a circle
2. Name the following using the polyhedron at the right.
Name 2 edges: ____________ _________________
Name a lateral face:_______________________
Name the bases:____________&____________
Name the vertices:_______________________
3. Draw an example of a pyramid
4. Draw an example of a prism
5. Name two differences between pyramids and prisms.
______________________________________________________________________________________________
______________________________________________________________________________________________
6. Using the views of a slid figure below, draw the back view of the figure.
7. The base of a prism is a regular hexagon that measures 5 cm on each side. The prism has a height of 12 cm. What
is its lateral area?
8. Find the surface area of a cylindrical water tank that is 5 meters tall and has a diameter of 8 meters.
9. Find the lateral area, surface area and volume of the cylinder below.
Lateral______________________
Total________________________
Volume______________________
10. Find the surface area of a square pyramid if the side lengths of the base is 13 cm and the slant height is 8cm.
11. Draw the net of each solid. Then name the solid.
12. Calculate the slant height, lateral area, total surface area, and volume of the right cone below.
L=_______________________
Lateral = __________________
Total = ___________________
Volume=__________________
13. Calculate the lateral area, total area and volume of the cylinder.
Lateral = __________________
Total = ___________________
Volume=__________________
14. If a spherical ballon has a great circle with a circumference of 16π inches, how much air is needed to fill it?
15. The volume of the larger prism is 128cm cubed. If the prisms are similar, What is the volume of the smaller
prism?
16. Find the volume of the hexagonal prism below. Remember to find the are of hexagon first!
17. Two cones are similar. If the ratio of their radii is 3:4, then
a) What is the ratio of their surface areas?
b) What is the ration of their volumes?
18. Name the following:
I.
Two lines containing point N___________________
II.
A segment containing point Q __________________
III.
A triangle_______________
IV.
How many great circles are shown? ____________
20. Compare Plane Eucliedean and Spherical Geometries.
Euclidean
Line
Triangle
Spherical
Name _________________________________
Geometry – Spring Semester Review (15-16)
Date ______________________
SEMESTER REVIEW: Chapter 11
For # 1-6, write the Area formula for the following polygons:
1. __________________Triangle
2. _________________ Parallelogram
3. _________________Trapezoid
4. _________________ Rhombus
5. _________________ Kite
6. _________________ Regular Polygon
For # 7 – 12, find the area of each polygon. Round answers to the nearest tenth.
13. If two figures are similar and the ratio of sides lengths is a:b, then the ratio of perimeters is
_________ and the ratio of areas is ______.
14. The ratio of areas of two similar figures is 144:49. Write the ratio of the lengths of the
corresponding sides.
15. Two triangles are similar. The smaller triangle has a side length of 4, while the larger has a
side length of 10. If the area of the larger triangle has an area of 200, what is the area of the
smaller triangle.
16. You have a great photo that is 3” by 5”. You want to enlarge the area of the picture using a scale
factor of 3. (11.3)
A) What is the area of the larger picture?
B) Will it fit on your 9 x 12 scrapbook page?
17. Find the exact and approximate circumference of a circle with a diameter of 50 inches.
Exact = ________________
Approximate:_______________
Formulas for Circles:
Area =
π r2
Circumference =
2π r or π d
Length of an arc =
N
• 2π r
360
For # 18 & 19, find the indicated measure.
18.
19.
20. Find the length of arc CD with an arc measure of 108 ° and a radius of 17 cm.
For # 21 & 22, find the indicated measure.
21.
22.
23. Find the area of a sector with an arc measure of 114 ° and a radius of 10 in.
Area of a Sector =
N
•π r2
360
Name _________________________________
Geometry – Spring Semester Review (15-16)
Date ______________________
SEMESTER REVIEW: Chapter 10
Solve for x:
1.
2.
x = ____
4.
x = ____
3.
x = ____
5.
x = ____
6.
x = ____
x = ____
For # 7 – 16, write the segment, ray, or line (using proper notation) that best describes the given part
of the circle.
17. If the measure of an arc is less than 180 ° , then the arc is a _____________ arc.
18. If the measure of an arc is greater than 180 ° , then the arc is a _______________ arc.
19. If the measure of an arc is equal to 180 ° , then the arc is a _________________.
20. The opposite angles in an inscribed quadrilateral are ______________________.
21. The circle is circumscribed by the pentagon as shown. If AB = 10, BC = 5, AI = 14, GF = 6,
and GE = 12. Find the following measures:
22. Find the value of x.
26. Find the m < ABC.
x = ____
m < ABC = ____
23. Find the radius of the circle.
27. Find the measure of arc ABC.
r = ____
arc ABC = ____
24. Find the measure of arc
AC.
28. Find the m < 2.
m < 2 = ____
arc AC = ____
25. Find the m < 1.
29. Find the measure of arc AC and the measure of arc
CD.
arc AC = ____
arc CD = ____
m < 1 = ____
In # 30-32, find the value of x.
30.
32.
x = ________
33.
x = ________
x = ________
33. How many common tangents do the two circles share?
Common Tangents: _________
34. Find the value of x and y.
35. Find the value of x and y.
36. Find KD.
37. Given: O , AC = 24. Find BD.
38. Write the equation of a circle with center (5, -2) and diameter is 3. Graph it.
Equation: _________________________
Name _________________________________
Geometry – Spring Semester Review (15-16)
Date ______________________
SEMESTER REVIEW: Chapter 8
1. What is the Pythagorean Formula? ______________________
2. Find the unknown side length of the right triangle. Write your answer in simplest radical form and decimal rounded to
the nearest hundredth.
(A) ______ = ______
(B) ______ = ______
(C) ______ = ______
3. Determine if the given measures are measures of the sides of a right triangle.
_______ 15, 36, 39
_______ 21, 72, 75
_______ 24, 46, 51
4. Find the geometric mean of 40 and 10. _______
5. Find the geometric mean of 6 and 9. _______
6. Find the value of x. Round your answers to the nearest hundredth.
(A) ___________
(B) ___________
(C) _____________
7. Find the missing measures. Write your answers in simplest radical form.
a.
a=______ b=________
b.
.
x=_____ y=______
c.
x=_____ y=______
8. Can the following measures be the sides of a triangle? If so, classify the triangles formed by the side lengths as acute,
right, or obtuse.
(A) 6, 8, 9 ___________________
(B) 10, 2 2 , 6 3 ___________________
(C) 15, 20, 5 ___________________
(D) 13, 18, 24 ___________________
Matching:
9-11) Match the following ratios: (3 pts each)
______ sin A
a)
______ cos A
b)
______ tan A
c)
opposite
adjacent
opposite
hypotenuse
adjacent
hypotenuse
12. Find the indicated ratio. Put answers in simplest form. (3 pts each)
Q
5
13
12
N
sin N = _______
sin Q = _______
cos N = _______
cos Q = _______
tan N = _______
tan Q = _______
For #13-16, use sine, cosine and tangent of angles to find the indicated lengths or angles. Round all lengths to the nearest
hundredth and all angles to the nearest degree. You must show work!
13.
14.
15.
16.
17. Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the
shadow to the top of the tree with respect to the ground? Draw figure. Round the answer to the nearest degree.
18. A kite’s string is 200 meters long. Find the altitude (height off the ground) at which the kite is flying if the string
makes an angle of 30 degrees with the ground. Draw a figure. Round the answer to the nearest hundredth.
19. A 16-foot ladder leaning against a building has an angle of depression of 68 ° . How far is the base of the ladder from
the base of the building? Round the answer to the nearest hundredth.
Name _________________________________
Geometry – Spring Semester Review (15-16)
Date ______________________
SEMESTER REVIEW: Chapter 7
1. Refer to the similar triangles.
10
A
B
y
X
Y
7
x
18
14
C
Z
Given: ∆ABC ∼ ∆XYZ.
4. Segments a, b, and c are parallel.
Find the value of x.
a. Write all pairs of congruent angles.
__________
___________
3. Alyssa wants to measure the height of the flagpole
school. She places a mirror on the ground 54 feet
from the flagpole, then walks backward until she is
able to see the top of the flagpole in the mirror.
Her eyes are 5.9 feet above the ground, and she is
14 feet from the mirror. What is the height of the
flagpole to the nearest tenth of a foot?
___________
a
b. Write the ratios of proportional sides.
________
=
________
=
________
b
x = ________
Im age
= _______
Original
23
20
c
c. What is the scale factor of ∆ABC to ∆XYZ?
S. F. =
27
x
5. Given: ∆ABC ∼ ∆ADE (not drawn to scale).
B
d. Write a proportion to solve for the values of x
and y. Then, find x and y.
x = ________
8
C
y = ________
D
A
12
AC = 8, and AE = 12.
E
If the perimeter of triangle ABC = 20, what is the
perimeter of triangle ADE
2. Given: ∆RST ∼ ∆RUV.
R
answer ____________
18
S
21
6
U
6. Given: DABC ~ DEDC (not drawn to scale).
AB = 1.5, BC = 2, and DE = 4.5.
T
12
y
Write a proportion to solve for the values of x
and y. Then, find x and y.
x = ________
y = ________
E
x
V
A
4.5
1.5
B
2
C
D
a. What is the perimeter of triangle DEC?
answer _____________
Name _________________________________
Geometry – Spring Semester Review (15-16)
Date ______________________
SEMESTER REVIEW: Chapter 6
1. Give the names for each polygon with the given number of sides:
3 sides __________________
7 sides __________________
4 sides __________________
8 sides __________________
5 sides __________________
9 sides __________________
6 sides __________________
10 sides__________________
2. Find the following for a regular hexagon:
3. Find the following for a regular 19-gon:
_________(A) The interior angle sum
________ (A) The interior angles sum
_________(B) The measure of each interior angle
________ (B) The measure of each interior angle
_________(C) The exterior angles sum
________ (C) The exterior angles sum
_________(D) The measure of each exterior angle
________ (D) The measure of each exterior angle
4. Put an X in the box if the shape always has the given property.
Property
All sides are congruent
Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
Exactly one pair of opposite sides are parallel
All angles are congruent
Exactly one pair of opposite angles are congruent
Diagonals are perpendicular
Diagonals are congruent
Diagonals bisect each other
Parallelogram
Rectangle
Rhombus
Square
Kite
Trapezoid
Square
Kite
Trapezoid
5. Given the following combinations of calculations, which figures can you identify?
Parallelogram
Distance formula only
Slope formula only
Either distance or slope
Both distance and slope are required
Rectangle
Rhombus