is the midsegment of Δqrs. find the value of...

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



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



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



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



reason.

11)


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



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



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



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



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°


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



reason.

11) Find the length of the midsegment of the trapezoid.


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



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



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.

9)

Copy

right

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ou

ghto

n M

iffl

in H

arco

urt

Pub

lish

ing

Co

mpan

y. A

ll r

ights

res

erv

ed.

Find the radius of circle L.

Find the circumference of circle

C.

2nd



reason.

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



reason.

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?

17) Find the geometric probability that a point randomly chosen in the

figure is in the shaded region?

18) Tell whether the solid is a polyhedron. If it is, find the number of

faces, vertices, and edges.

19) 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



reason.

7)

20) Describe the shape that is formed by the cut made in the food

shown.

21)

22)

23)

24)

25)

26)

27)

28)

29)

30)

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)

2nd



reason.

Q R is a radius of R and P Q is tangent to R. Find the value of x.

3)

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) m KLN

6) m JN L

7) m LM

Find the measure of the given arc.

8) m AC

9) m Q RS

Find the value(s) of the variable(s).

10)

11)

2nd



reason.

12)

13)

14)

15)

16) Write the standard equation of a circle with a center of (-5, 4) and

has a radius of 6.

17) Write the standard equation of a circle that has a center of (4, –8)

and a point on the circle of (6, –2).

18) Graph the equation 22

3 6.25x y

is the midsegment of Δqrs. find the value of...

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