concepts geometry 2nd semester review packet: completed

Concepts Geometry 2nd

Semester Review Packet: Completed review packets are worth 20

points extra credit and are due the day of the exam. Late review packets will not be

accepted for any reason!

Circle the correct term to complete each sentence.

1) A (centroid, median of a triangle) is a segment whose endpoints are a

vertex and the midpoint of the side opposite the vertex.

2) The (altitude, median) of a triangle is a perpendicular segment from a

vertex to the line containing the side opposite the vertex.

3) To write a(n) (indirect proof, negation), you start by assuming that

the opposite of what you want to prove is true.

4) A point where three lines intersect is a (point of concurrency, incenter).

5) In the diagram, ST and TU are midsegments of triangle PQR. Find PR

and TU.

6) In the digram, ED and DF are midsegments of triangle ABC. Find DF

and AB.

7) Draw a perpendicular bisector that bisects BC in the triangle below.

8) Draw an angle bisector at vertex A in the triangle below.

3X - 4

5X+2

A

C

B

C

A

B





Name each figure in BDF .

9) An angle bisector

10) A median

11) A perpendicular bisector

12) An altitude

13) Write the inverse of the conditional statement, “If an angle is obtuse,

then its measure is greater than 90 and less than 180.”

14) Write the contrapositive of the conditional statement, “If an angle is

obtuse, then its measure is greater than 90 and less than 180.”

15) Write the negation of the statement, “The figure is a triangle.”

Is it possible for a triangle to have sides with the given lengths? Explain.

16) 5 in., 8 in., 15 in.

17) 20 m, 22m, 24 m

18) Write a convincing argument that uses indirect reasoning to show that

a triangle can have at most one obtuse angle.

19) List the angles and sides in order from smallest to largest.

In the figure, P is the centroid of Δ ABC and BP = 8.

20) Find the length of BF .

21) Find the length of FP .

B C

B B

D

E

F G

A

70o

80o

T

S

R





22) State the six properties of parallelograms.

True or False. Write the word „true‟ or „false‟ to each statement. Justify

your response.

23) All squares are rectangles.

24) A trapezoid is a parallelogram.

25) A rhombus can be a kite.

26) Some parallelograms are squares.

27) Every quadrilateral is a parallelogram.

28) Every rhombus is a square.

Fill in the blank for each definition with the appropriate word from the

Word Bank.

29) A(n)__________________ is a parallelogram with four right

angles.

30) A(n)__________________ is aquadrilateral with two pairs of

adjacent sides congruent and no opposite sides congruent.

31) Angles of a polygon that share a common side are _______________.

32) A(n)___________________ is a quadrilateral with exactly one

pair of parallel sides.

33) A(n)________________ is a parallelogram with four

congruent sides.





34) The _________________ of a trapezoid is the segment that

joins the midpoints of the nonparallel opposite sides.

35) A(n)__________________ is a quadrilateral with both pairs

of opposite sides parallel.

36) A(n)__________________ is a parallelogram with four

congruent sides and four right angles.

37) A(n)_____________________ is a trapezoid whose

nonparallel opposite sides are congruent.

38) Two angles that share a base of a trapezoid are its

_____________.

Work Bank: parallelogram skew trapezoid square

Base angles isosceles trapezoid rectangle consecutive angles

Kite rhombus circle ellipse midsegment

39) Draw and label a parallelogram. Name all the congruent sides

and angles. Draw in the diagonals.

40) How are a kite and a rhombus similar? How are they different?

41) In the rhombus below, find the variables and then find the side

lengths.

2x + 3

5y + 2

3y + 8 3x - 4





Use parallelogram ABCD for the following questions.

42) If the 2 100m ABC x and the 6 84m AD C x , find m BC D .

43) If AE = 3x, BD = 2y, CE = x + 8, and DE = 6y – 40, find x and y.

44) Find the measure of the numbered angles in the rhombus.

45) LMNP is a rectangle. Find the value of x and the length of each

LN = 3x + 1 and MP = 8x – 4

46) Suppose the diagonals of a parallelogram are both perpendicular

and congruent. What type of special quadrilateral is it? Explain your

reasoning.

47) Find the length of median MN if AB = 8 and DC = 16.

A

E

D C

B

A

D

M

C

N

B

50o

1

4 3

2





48) Find the length of AB if DC = 24 and MN = 13.

49) Use trapezoid ABCD to answer the following questions. Show all

work. EF is a midsegment.

If ooooyCmyBmxDmxAm )70(,,)12(,)2( , find measure

of all four angles.

50) Find the area of the parallelogram.

51) The area of a parallelogram is 24 in.2 and the height is 6 in. Find the

corresponding base.

52) Find the area of the triangle.

C

N

B A

M

D

E

D

A

F

B

C

6 cm

14 m

9 m

7.3 cm





53) An isosceles right triangle has area of 98 cm2. Find the length

of each leg.

54) A right triangle has legs of length 16 and 30. Find the length of

the hypotenuse.

55) Does the set of numbers 4, 5, 6 form a Pythagorean triple?

Explain.

56) Find the value of x. Leave your answer in simplest radical form.

57) A baseball diamond is a square with 90-ft sides. Home plate and

second base are at opposite vertices of the square. About how far is

home plate from second base?

58) The lengths of the sides of a triangle are 15, 8, 21. Classify the

triangle as acute, right, or obtuse.

59) The lengths of the sides of a triangle are 11, 12, 15. Classify the

triangle as acute, right, or obtuse.

x

10 ft

12 ft





60) Find the length of the hypotenuse of a 45-45-90 triangle with

legs of length 65 .

61) Find the length of a leg of a 45-45-90 triangle with a hypotenuse of

24.

62) Find the lengths of the legs of a 30-60-90 triangle with

hypotenuse of length 34 .

63) The longer leg of a 30-60-90 triangle has length 18. Find the

lengths of the shorter leg and the hypotenuse.

64) A car window is shaped like the trapezoid shown. Find the area

of the window.

65) Find the area of the kite with a diagonals of 7m and 9m.

66) Simplify 105

67) Simplify 8

28

18 in.

36 in.

20 in.





68) The perimeter of an equilateral triangle is 60 m. Its height is 17.3

m. What is its area?

a) 173 m2

b) 200 m2

c) 348 m2

d) 1044 m2

69) The area of a kite is 120 cm2. The length of one diagonal is 20 cm.

What is the length of the other diagonal?

a) 12 cm

b) 24 cm

c) 20 cm

d) 48 cm

70) Find the area of a regular pentagon with a 12.3 in. apothem and 8 in.

sides.

71) 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.

72) Explain, using complete sentences, why the radius of a regular polygon

is greater than the apothem. You may use a diagram as part of your

explanation.





73) Identify the following in circle O.

a) a minor arc

b) A semicircle

c) A major arc

d) A pair of congruent angles

e) A pair of adjacent arcs

f) m D C

g) m AOD

74) Using the above figure, if the radius of circle O is 4 m, what the

length of DC ?

75) Find the length of a semicircle with radius 1.3 m. Leave your answer in

terms of π.

76) Find the circumference of a circle with a diameter of 20 cm. Leave

your answer in terms of π.

77) Find the circumference of a circle with a radius of 29 cm. Leave your

answer in terms of π.

78) How much more pizza is in a 12 in. diameter pizza than in a 10 in pizza?

85o

D

C B

A

O





79) Find the area of a circle with a diameter of 6 m. leave your answer in

terms of π.

80) Find the area of sector TOP in circle O using a radius of 5 m and

90o

mTP .

81) A circle has an 8 in. radius. Find the area of a sector whose arc

measures 135. Leave your answer in terms of π.

82) Find the area of the shaded region. The diameter of the circle is 12

m.

83) Find the area of the shaded region.

3

3

1 1

1

1





I II

IV III

10” 30”

15”

10”

84) If a dart randomly hits the board, what is the probability that it will

hit in region II?

85) Find the probability that a

randomly chosen point in the

figure lies in the shaded

region.

86) Solve the proportion: 3

6

5

3

x.

87) Are the polygons similar? If so, give the similarity ratio of the first

polygon to the second. If not, explain.

88) The scale of a scale drawing is 2in. = .5 ft. The shorter diagonal of a

kite is 5 in. long on the scale drawing. Find the actual length of the

kite‟s diagonal.

4 in.

6

12

H G

F E 4

8

D C

B A





89) Explain why the triangles are similar. Then find the value of x.

90) Find the geometric mean of 9 and 4.

91) Find the geometric mean of 3 and 27.

92)

93)

94) Find the length of VX using the side-splitter theorem.

x

4

5

15





95) Find the value of x in the figure below.

96) The panels in the sail are parallel. Find the length of x and y.

97) The similarity ratio of two similar triangles is 3:7. The area of the

smaller triangle is 36 cm2. What is the area of the larger triangle?

concepts geometry 2nd semester review packet: completed

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