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TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #1
Given: GK  KI and GHL  IHL . Fill in each blank with
G
the word(s) or segment that best complete(s) each statement.
a. JK is a(n) _____________________.
K
L
J
b. __________ is an angle bisector.
M
H
c. __________ is a median.
d. MH is a(n) _______________________.
I
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #1
Given: GK  KI and GHL  IHL . Fill in each blank with
G
the word(s) or segment that best complete(s) each statement.
a. JK is a(n) _____________________.
K
L
J
b. __________ is an angle bisector.
c. __________ is a median.
d. MH is a(n) _______________________.
M
H
I
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #2
a. The measures of the angles of a triangle are in the extended ratio 2 : 4 : 6. Find the sum of the
smallest angle and the largest angle.
b. How many sides does a polygon have if the measure of each of its exterior angles is 22.5 ?
c. The supplement of an angle is 8 more than five times larger than the angle. Find the positive
difference between the angle and its supplement.
d. The area of a rhombus is 288 m2. Find the length of the two diagonals if their ratio is 2:1.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #2
a. The measures of the angles of a triangle are in the extended ratio 2 : 4 : 6. Find the sum of the
smallest angle and the largest angle.
b. How many sides does a polygon have if the measure of each of its exterior angles is 22.5 ?
c. The supplement of an angle is 8 more than five times larger than the angle. Find the positive
difference between the angle and its supplement.
d. The area of a rhombus is 288 m2. Find the length of the two diagonals if their ratio is 2:1.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #3
Determine whether each statement is always, sometimes, or never true.
a. The contrapositive of a conditional statement is true.
b. Four points lie in exactly one plane.
c. Supplementary angles form a linear pair.
d. A scalene triangle is obtuse.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #3
Determine whether each statement is always, sometimes, or never true.
a. The contrapositive of a conditional statement is true.
b. Four points lie in exactly one plane.
c. Supplementary angles form a linear pair.
d. A scalene triangle is obtuse.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #4
The diagonals of a rhombus are 8 ft and 12 ft. An equilateral triangle has an area of 16 3 cm2.
a. Find the perimeter of the rhombus.
b. Find the area of the rhombus.
c. Find the perimeter of the triangle.
d. Find the height of the triangle.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #4
The diagonals of a rhombus are 8 ft and 12 ft. An equilateral triangle has an area of 16 3 cm2.
a. Find the perimeter of the rhombus.
b. Find the area of the rhombus.
c. Find the perimeter of the triangle.
d. Find the height of the triangle.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #5
a. Find the number of sides of a nonagon plus the number of sides of a heptagon.
b. Find the number of sides of the regular polygon with interior angle measures of 156  .

 40 
c. Find the number of sides of the regular polygon with exterior angle measures of   .
 3 
d. Let x = the sum of the measures of the exterior angles of an octagon and let y = the measure of
one exterior angle of a regular decagon. Find x – y.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #5
a. Find the number of sides of a nonagon plus the number of sides of a heptagon.
b. Find the number of sides of the regular polygon with interior angle measures of 156  .

 40 
c. Find the number of sides of the regular polygon with exterior angle measures of   .
 3 
d. Let x = the sum of the measures of the exterior angles of an octagon and let y = the measure of
one exterior angle of a regular decagon. Find x – y.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #6
m6  3x  5 , m1  x  20 , and m5  145 


a. Find m6 .
b. Find m4 .
EB  EC ; AEC and DEC form a linear pair.
c. Find mDEB .
d. What is the measure of the angle that is vertical to AEC ?
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #6
m6  3x  5 , m1  x  20 , and m5  145 


a. Find m6 .
b. Find m4 .
EB  EC ; AEC and DEC form a linear pair.
c. Find mDEB .
d. What is the measure of the angle that is vertical to AEC ?
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #7
a. The lengths of two sides in a triangle are x and x + 9. The length of the third side must be greater
than _________ and less than _________.
b. A board 2 feet long is cut into two pieces in the ratio 1:2. Find the length of the longer piece in
inches.
c. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 14 in and
18 in long. Find the length of the altitude to the hypotenuse.
d. What postulate or theorem can be used to prove the two triangles shown are congruent?
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #7
a. The lengths of two sides in a triangle are x and x + 9. The length of the third side must be greater
than _________ and less than _________.
b. A board 2 feet long is cut into two pieces in the ratio 1:2. Find the length of the longer piece in
inches.
c. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 14 in and
18 in long. Find the length of the altitude to the hypotenuse.
d. What postulate or theorem can be used to prove the two triangles shown are congruent?
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #8
Find each indicated measure.
a. m1  m2
104 
b. m3  m4
2
1
27 
c. m3  m5
3
4
d. m2  m6
76 
6
5
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #8
Find each indicated measure.
a. m1  m2
104 
b. m3  m4
2
1
27 
c. m3  m5
3
4
d. m2  m6
76 
6
5
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #9
The vertices of a triangle are formed by A3,2 , B 5,4, and C 5,2 .
a. Find the coordinates of point D such that AD  BD  CD .
b. Find the coordinates of point E such that E is equidistant from the sides of ABC .
c. Find the coordinates of point F such that AF 
2
AM , where M is the midpoint of BC .
3
d. Find the coordinates of point G, the orthocenter of ABC .
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #9
The vertices of a triangle are formed by A3,2 , B 5,4, and C 5,2 .
a. Find the coordinates of point D such that AD  BD  CD .
b. Find the coordinates of point E such that E is equidistant from the sides of ABC .
c. Find the coordinates of point F such that AF 
2
AM , where M is the midpoint of BC .
3
d. Find the coordinates of point G, the orthocenter of ABC .
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #10
Given: SFU  SUF , mFUO  mFWO , mS  138  , mUFW  47  , and the exterior angle
mUON  107  .
a. Find mSFU .
138
b. Find mSUO .
c. Find mW .
d. Find mWFS .
21
47 
21
120 
120 
73 107 
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #10
Given: SFU  SUF , mFUO  mFWO , mS  138  , mUFW  47  , and the exterior angle
mUON  107  .
a. Find mSFU .
138
b. Find mSUO .
c. Find mW .
d. Find mWFS .
21
47 
120 
21
120 
73 107 
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #11
a. Calculate the cosine of Q in right PQR where PR  15 , PQ  17 , and mR  90  .
b. Calculate the area of an equilateral triangle inscribed in a circle with radius 6.
c. If nine businessmen attended a meeting and all shook hands with one another twice (once for
introductions and again later to say goodbye), how many handshakes were exchanged?
d. A rectangle has an area of 120 square units. Its length and width are whole numbers of units.
What are the dimensions of the rectangle with the smallest perimeter that is greater than 60 units?
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #11
a. Calculate the cosine of Q in right PQR where PR  15 , PQ  17 , and mR  90  .
b. Calculate the area of an equilateral triangle inscribed in a circle with radius 6.
c. If nine businessmen attended a meeting and all shook hands with one another twice (once for
introductions and again later to say goodbye), how many handshakes were exchanged?
d. A rectangle has an area of 120 square units. Its length and width are whole numbers of units.
What are the dimensions of the rectangle with the smallest perimeter that is greater than 60 units?
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #12
a. Two supplementary angles have measures 5 x  28 and 11x  64  . Find the measure of the
smaller of the two angles.


b. The average of three interior angles in a pentagon is 139  . The remaining two interior angles have
equal measures. Find the measure of one of the remaining interior angles.
c. The measure of an interior angle of a regular polygon is 36 more than its adjacent exterior angle.
How many sides does the polygon have?
d. B, E, and F are midpoints of the sides of ADC . Given that AD = 12, DC = 22, and AC = 28, find
the perimeter of EFB .
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #12
a. Two supplementary angles have measures 5 x  28 and 11x  64  . Find the measure of the
smaller of the two angles.


b. The average of three interior angles in a pentagon is 139  . The remaining two interior angles have
equal measures. Find the measure of one of the remaining interior angles.
c. The measure of an interior angle of a regular polygon is 36 more than its adjacent exterior angle.
How many sides does the polygon have?
d. B, E, and F are midpoints of the sides of ADC . Given that AD = 12, DC = 22, and AC = 28, find
the perimeter of EFB .
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #13
a. The diagonal of one face of a cube is 8 cm. Find the total surface area of the cube.
b. Caitlin laid out stones for a necklace in a big circle, with each stone spaced an equal distance
apart. She then counted the stones in order around the circle, but before should could finish she lost
track of where she had started. Not wanting to start counting again, she was able to determine the
number of stones in the necklace because she knows the sixth stone was directly opposite the
seventeenth stone. How many stones are in the necklace?
c. Z is the circumcenter of WXY . Find XZ + YX.
d. Find the radius of a circle in which the perimeter of an inscribed square is 20 in.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #13
a. The diagonal of one face of a cube is 8 cm. Find the total surface area of the cube.
b. Caitlin laid out stones for a necklace in a big circle, with each stone spaced an equal distance
apart. She then counted the stones in order around the circle, but before should could finish she lost
track of where she had started. Not wanting to start counting again, she was able to determine the
number of stones in the necklace because she knows the sixth stone was directly opposite the
seventeenth stone. How many stones are in the necklace?
c. Z is the circumcenter of WXY . Find XZ + YX.
d. Find the radius of a circle in which the perimeter of an inscribed square is 20 in.
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #14
a. If FEBC is a square and EF = 4 cm, find the perimeter of ADEF.
b. Give the most specific name of XYZW given that XW  ZW and XY  ZY .
c. Congruent circular disks are stamped out of a square sheet of metal as
shown. How many square inches of waste sheet metal are left after the disks
are stamped out?
for part c
d. Given the diagram, what is 2m4  m3  3m1  2m2  m5 ?
for part d -------------
TALAHASSEE STATEWIDE
1/14/2017
GEOMETRY TEAM QUESTION #14
a. If FEBC is a square and EF = 4 cm, find the perimeter of ADEF.
b. Give the most specific name of XYZW given that XW  ZW and XY  ZY .
c. Congruent circular disks are stamped out of a square sheet of metal as
shown. How many square inches of waste sheet metal are left after the disks
are stamped out?
d. Given the diagram, what is 2m4  m3  3m1  2m2  m5 ?
for part d -------------
for part c