2 nd Semester Geometry Review Packet: Completed Review packets are due at the exam and are worth 20 extra credit points. Late review packets will not be accepted for any reason. WY is the midsegment of ΔQRS. Find the value of x. 1) 2) 3) Find the value of x. 4) 5) In the diagram, the perpendicular bisectors of ΔWXY meet at point Z. Find the indicated measure. 6) WZ 7) ZY
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2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
W Y is the midsegment of ΔQRS. Find the value of x.
1) 2)
3)
Find the value of x.
4)
5)
In the diagram, the perpendicular bisectors of ΔWXY meet at point Z.
Find the indicated measure.
6) WZ 7) ZY
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
Find the coordinates of the centroid P of ΔSTU.
8) S(2, 5), T(5, –2), U(–1, –6)
9) S(–1, 7), T(5, –6), U(–7, –4)
In ΔABC, Q is the centroid. Find the indicated length.
10) QC = 12. Find QM. 11) QC = 6. Find CL.
List the sides and the angles in order from smallest to largest.
12)
13)
Is it possible to construct a triangle with the given side lengths? Justify
your answer.
14)10, 7, 13
15)26, 20, 2
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
Describe the possible lengths of the third side of the triangle
given the lengths of the other two sides.
16) 5 inches, 6 inches
17) 14 feet, 21 feet
Copy and complete with <, >, or =.
18) AB_____ BC 19) RS _____ VU
20) Suppose you wanted to prove the statement “If x + y > 20 and y = 5,
then x > 15.” What temporary assumption could you make to
prove the conclusion indirectly?
Use the Hinge Theorem or its converse and properties of triangles to
write and solve an inequality to describe a restriction on the value of x.
21) 22)
In the diagram, ABCDE ~ FGHJK.
1) Find the value of x.
2) Find the perimeter of ABCDE.
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
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)
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
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 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?
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
16) Plot the coordinate on the coordinate plane and find coordinate for point
E so that ~ABC AD E .
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 ____________________.
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.
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
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)
6)
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)
14)
x
12 8
4
6
y
x
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
15)
Find the value of each variable. Write your answers in simplest radical
form.
16)
17)
18)
19)
20)
21) Each half of the drawbridge is about 290 feet long. How high does a
seagull who is on the end of the drawbridge rise when the angle with
measure xo is 30o? 45o?, 60o?
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?
12 3
x y
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
Find the sum of the measures of the interior angles of the indicated
convex polygon.
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.
5)
6)
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.
8)
9)
10)
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
11) Find the length of the midsegment of the trapezoid.
Find the value of x.
12)
13)
Give the most specific name for the quadrilateral. Explain your answer.
14)
15)
16)
17) In the kite JKLM, find the measure of K .
2nd
Semester Geometry Review Packet: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
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: Completed Review packets are due at the exam
and are worth 20 extra credit points. Late review packets will not be accepted for any
reason.
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.