in the diagram, abcde fghjk - mrs. sowatsky's...
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2nd
Semester Geometry Review Packet
In the diagram, ABCDE ~ FGHJK.
1) Find the value of x.
2) Find the perimeter of ABCDE.
Determine whether the triangles are similar. If so, write
a similarity statement and the postulate or theorem that
justifies your answer.
6)
7)
Determine the value of x that makes ΔABC ~ ΔXYZ.
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9)
In Exercises 10 and 11, find the length of AB .
2nd
Semester Geometry Review Packet
10)
11)
Find the value of x.
12)
13) The panels in the sail are parallel. Find the length of x and y.
14) The perimeter of a rectangular corn field is 440 meters. The ratio
of its length to its width is 7:4. What is the length and width of
the field?
2nd
Semester Geometry Review Packet
15) A cellular telephone tower casts a shadow that is 72 feet long, while a
tree nearby that is 27 feet tall casts a shadow that is 6 feet long. How tall
is the tower?
16) Plot the coordinate on the coordinate plane and find coordinate for point
E so that ~ABC ADE .
A(0, 0), B(0, 6), C(3, 0), D(0, 9), E(x, y)
17) You are making a scale model of your school’s baseball diamond as part of
an art project. The distance between two consecutive bases is 90 feet. If
you use a scale factor of 1/180 to build your model, what will be the distance
around the bases on your model?
Short Answer: Answer the following questions completely.
18) If two polygons are congruent, must they be similar? If two polygons are
similar, must they be congruent? Explain your answer.
19) Explain why all equilateral triangles are similar. Include sketches in your
answer.
20) How can you show that two triangles are similar?
Fill-in the blank with the most appropriate word to complete the sentence.
1) A set of three positive integers a, b, and c that satisfy the equation 222 bac is called a ____________________.
2nd
Semester Geometry Review Packet
2) The longest side of a right triangle is called the
_________________.
3) Two triangles are ______________ if their corresponding angles are
congruent and their corresponding side lengths are proportional.
4) A triangle with two congruent sides and a right angle is called an
_____________________.
Find the unknown side length. Write your answer in simplest radical
form.
5)
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7)
Classify the triangle formed by the side lengths as right,acute, or
obtuse.
8) 4, 5, 6
9) 11, 13, 23
10) 8, 8 3 , 16
11) Find the area of the isosceles triangle.
12) Find the geometric mean of 3 and 7.
Solve for the missing variable(s).
13)
x
2nd
Semester Geometry Review Packet
14)
15)
Find the value of each variable. Write your answers in simplest radical
form.
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23) In baseball, the distance of the paths between each pair of consecutive
bases is 90 feet and the paths form right angles. How far does the ball need
to travel if it is thrown from home plate directly to second base?
Find the sum of the measures of the interior angles of the indicated
convex polygon.
12 8
4
6
y
x
12 3
x y
2nd
Semester Geometry Review Packet
1) Decagon
2) 18-gon
The sum of the measures of the interior angles of a convex polygon is
given. Classify the polygon by the number of sides.
3) 1080°
4) 3960°
Find the value of x.
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7) The measure of one interior angle of a parallelogram is 42 degrees more
than twice the measure of another angle. Find the measure of each angle.
Find the value of the variables in the parallelogram.
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11) Find the length of the midsegment of the trapezoid.
2nd
Semester Geometry Review Packet
Find the value of x.
12)
13)
Give the most specific name for the quadrilateral. Explain your answer.
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17) In the kite JKLM, find the measure of K .
2nd
Semester Geometry Review Packet
18) Short Answer: Answer two questions fully with complete sentences.
a) In parallelogram ABCD, the measure of angle A is 65 degrees. Explain how
you would find the other angles measures of parallelogram ABCD.
b) A quadrilateral has four congruent sides. Is the quadrilateral a
parallelogram? Justify your answer.
c) The diagonals of a rhombus are 6 inches and 8 inches. What is the
perimeter of the rhombus? Explain.
d) Explain why a parallelogram with one right angle must be a rectangle.
Use the diagram to find the indicated measure.
1) Find the circumference.
2) Find the radius.
Find the length of . Round answers to the nearest tenth.
3)
4)
C = 113 km
JK
2nd
Semester Geometry Review Packet
Find the indicated measure. Round answers to the nearest tenth.
5)
6)
Find the area of the sector. Round to the nearest tenth.
7)
8)
Find the area of the regular polygon. Round to the nearest tenth.
9)
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Find the radius of circle L.
Find the circumference of circle
C.
2nd
Semester Geometry Review Packet
10) A circle with a diameter of 10 in. contains an inscribed square as
shown below. Find the area of the shaded region. Leave your answer in
terms of π.
11)
12) A circle has an 8 in. radius. Find the area of a sector whose arc
measures 135. Leave your answer in terms of π.
13) How much more pizza is in a 12 in. diameter pizza than in a 10 in pizza?
14) Find the area of a regular pentagon with a 12.3 in. apothem and 8 in.
sides.
3
3
1 1
1
1
2nd
Semester Geometry Review Packet
I II
IV III
10” 30”
15”
10”
15) A gazebo is built in the shape of a regular octagon. Each side is 8 ft
long, and its apothem is 9.7 feet. To the nearest tenth, find the area
enclosed by the gazebo.
16) If a dart randomly hits the board, what is the probability that it will
hit in region II?
Tell whether the solid is a polyhedron. If it is, find the number of faces,
vertices, and edges.
1) 2)
Use Euler’s Theorem to find the value of n.
3) Faces: 8, Vertices: 12, Edges: n
4) Faces: 9, Vertices: n, Edges: 21
5) Faces: n, Vertices: 16, Edges: 24
Find the surface area and volume of the solid. The pyramids are
regular and the prisms, cones, and cylinders are right. Round your
answers to two decimal places, if necessary.
6)
2nd
Semester Geometry Review Packet
17) Describe the shape that is formed by the cut made in the food shown.
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14) The surface area of a lacrosse ball is approximately 20 square
inches. What is the diameter of the ball?
Tell how many common tangents the given circles have. Then draw the
common tangents.
1)
2)
QR is a radius of R and PQ is tangent to R. Find the value of x.
3)
2nd
Semester Geometry Review Packet
4)
JM and KN are diameters of P. Identify the given arc as a major
arc, minor arc, or semicircle. Then find the measure of the arc.
5) mKLN
6) mJNL
7) mLM
Find the measure of the given arc.
8) mAC
9) mQRS
Find the value(s) of the variable(s).
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