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Honors Geometry Review Packet 2015
Note: Exam will include problems from 11.5-11.8 that are not included on this packet
PQR ~ CDE .
1) List all pairs of congruent angles.
2) Write the ratios of the corresponding sides in
a statement of proportionality.
In the diagram, ABCDE ~ FGHJK.
3) Find the value of x.
4) 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.
8)
9)
In Exercises 10 and 11, find the length of AB .
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?
15) A cellular telephone tower casts a shadow that is 24 meters long, while a
tree nearby that is 9 meters tall casts a shadow that is 2 meters 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?
18) You take 450 U.S. dollars to the bank to exchange for European euros.
The exchange rate on that day is about 0.82 euros per U.S. dollar.
How many European euros did you get for the 450 U.S. dollars?
Short Answer: Answer the following questions completely.
19) If two polygons are congruent, must they be similar? If two polygons are
similar, must they be congruent? Explain your answer.
20) Explain why all equilateral triangles are similar. Include sketches in your
answer.
21) Explain how the side lengths of a triangle can be used to classify it as
acute, right, or obtuse.
22)
Explain why the acute angles in an isosceles right triangle
always measure 45o.
23)
Explain when to use a trigonometric ratio to find a side length
of a right triangle and when to use the Pythagorean Theorem.
Find the value of x. Write your answer in simplest radical form.
24)
25)
Classify the triangle as acute, right, or obtuse.
26) 3, 5, 34
27) 9,15,10 3
Find the exact value of x.
28)
29)
Find the value of each variable. Keep your answer in simplest radical form.
30)
31)
Solve the right triangle. Round your answer to the nearest tenth.
32)
33)
34) A balloon rises to the ceiling of a gymnasium. You want to find the
distance from the ground to the balloon. You use a cardboard square
to line up the balloon and the ground. Your friend measures the
vertical distance from the ground to your eye and the distance from
you to the gym wall. Approximate the distance from the ground to
the balloon.
35) A soccer ball is placed 10 feet away from the goal, which is 8 feet high.
You kick the ball and it hits the crossbar along the top of the goal. What is
the angle of elevation of your kick?
36) The shadow of a telephone pole is 20 feet long. You measure the
angle of elevation from the end of the shadow to the top of the
telephone pole to be 70°. What is the height of the telephone pole?
Round your answer to the nearest foot.
Find the sum of the measures of the interior angles of the indicated
convex polygon.
37) Decagon
38) 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.
39) 1080°
40) 3960°
Find the value of x.
41)
42)
43) 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 x in the parallelogram.
44)
45)
Find the value of x.
46)
47)
Give the most specific name for the quadrilateral.
48)
49)
50)
51) In the kite shown, m  ADC = 105° and m  DAB = 100°. Find m  DCB.
Short Answer: Answer each question fully with complete sentences.
52) Explain why any two regular pentagons are similar.
53) In parallelogram ABCD, the measure of angle A is 65 degrees. Explain
how you would find the other angles measures of parallelogram ABCD.
54) A quadrilateral has four congruent sides. Is the quadrilateral a
parallelogram? Justify your answer.
55) The diagonals of a rhombus are 6 inches and 8 inches. What is the
perimeter of the rhombus? Explain.
56) Explain why a parallelogram with one right angles must be a rectangle.
Tell how many common tangents the given circles have. Then draw the
common tangents.
57)
58)
QR is a radius of
R and PQ is tangent to
R. Find the value of x.
59)
60)
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.
61) mKLN
62) mJNL
63) mLM
Find the measure of the given arc.
64) mAC
65) mQRS
Find the value(s) of the variable(s).
66)
67)
68)
69)
70)
71)
72) Write the standard equation of a circle with a center of (-5, 4) and
has a radius of 6.
73) Write the standard equation of a circle that has a center of (4, –8)
and a point on the circle of (6, –2).
74) Graph the equation x 2   y  3  6.25
2
Use the diagram to find the indicated measure.
75) Find the circumference.
A = 17.64π m2
76) Find the radius.
C = 100 ft
Find the indicated measure. Round answers to the nearest tenth.
78) Length of AB
79) Circumference of
L
The area of D is 113.1 square meters. The area of sector ADB is 34.6
square meters. Find the indicated measure.
80) Radius of
D
81) Circumference of
82) m AB
83) Length ofACB
D
Find the area of the shaded region. Round answers to the nearest tenth, if
necessary.
84)
85)
86)
87)
Find the probability that a randomly chosen point in the figure lies in the
shaded region.
88)
89)
90) A measuring wheel is used to calculate the length of a path. The
diameter of the wheel is 8 cm. The wheel rotates 87 times along the length
of the path. About how long is the path?
91) The area of a circular pond is about 138,656 square meters. You are
going to walk around the entire edge of the pond. About how far will you
walk? Give your answer to the nearest meter.
92) Basaltic columns are geological formations that result from rapidly
cooling lava. The Giant’s Causeway in Ireland contains many hexagonal
columns. Suppose that one of the columns is in the shape of a regular
hexagon with radius 8 inches. What is the apothem of the column? Find the
perimeter and area of the column. Round the area to the nearest square
inch.