2D Geometry Questions and Answers

Find the coordinates of a point on a circle with radius 15 corresponding to an angle of 80 x y Round your answers to three decimal places

Question 1 Points 2 If the point 9 5 is translated 6 units left and 5 units up then find the translated coordinates of the point O 3 10 O 3 10 O 3 10 O 3 10

2 Graph h x x 3 1 Describe transformation

3 Find the volume of each solid Then list these solids in order from the one with the least volume to the one with the greatest volume Part I Give the volume of each solid Show your work A a cube with edge 5 cm B a cylinder with a radius of 4 cm and a height of 4 cm C a square pyramid with base edges 6 cm and height 6 cm D a cone with a radius 4 cm and height 9 cm E a rectangular prism with a 5 cm by 5 cm base and height 6 cm Part II list these solids in order from the one with the least volume to the one with the greatest volume

4 Three balls are packaged in a cylindrical container as shown below The balls just touch the top bottom and sides of the cylinder The diameter of each ball is 13 cm a What is the volume of the cylinder Explain your method for finding the volume b What is the total volume of the three balls Explain your method for finding the total volume c What percent of the volume

2 An ice cream vendor presses a sphere of frozen yogurt into a cone as shown below If the yogurt melts into the cone will the cone overflow Explain and show work Note The diameter of the scoop is 8 cm and the height of the cone is 8 cm 12 cm

3 Eric has a trolley He wants to use that trolley to transport wooden blocks The size of the trolley is 3 960 000 square centimeters He found the wooden blocks to have a density of 0 0029 blocks per square centimeter How many total wooden blocks can he carry in the trolley

4 The volumes of two similar figures are 216 cm and 1728 cm The surface area of the larger figure is 864 cm Find the surface area of t smaller figure

2 The Pyramid of Khufu is a square pyramid which had a side length of about 230 m and a height of about 147 m when it was completed The Pyramid of Khafre had a side length of about 215 m and a height of about 144 m when it was completed What was the approximate difference in the volume of the two pyramids upon completion

4 6 Given Point is the midpoint of AC Point C is the midpoint of AD Prove 4AB AD Arrange the steps in order to complete the proof 1 2 3 4 G 5 Use the figure to complete the proof of the theorem 1 21 22 2 21 and 22 form a linear pair 3 21 and 22 are supplementary 4 21 and 22 are right angles If two congruent angles form a linear pair then they are right angles Given 21 22 Prove m 1 Given 2 3 4 Blank 2 Point is the midpoint of AC Point C is the midpoint of AD Given AABAD Addition AB AB AD 4 ABAD Substitution CD Definition of midpoint AC CD AD Segment Addition Postulate it is given that Z21 22 Also 2123 because these are ABBC AC All 4 BC AC AB AB AC AC AC AD Substitution Blank 1 options corresponding vertical angles Therefore 22 23 by the Transitive Property of Congruence by the Blank 1 2 OPTIONS Linear pairs are suppl Oliven If 2s are and suppl then they are right s Blank 2 options Converse of Corresponding Angles Theorem Converse of Alternate Exterior Angles Theorem that m

3 A box measures 10 in wide 12 in high and 14 in deep If all surfaces are made of cardboard how much cardboard is used to make the box Show your work

1 For a d use the diagram below 4 cm 4 cm 4 cm 4 cm 4 cm 4 cm 9 cm a Classify the prism b Find the lateral area of the prism c The bases are regular hexagons They are of each is about 41 6 cm Find the sum of their d Find the surface area of the prism

2 Given that AJKL AGKH solve for x K G 4 6 X H L

Question 9 Points 1 Which of the following transformation carry the given regular polygon onto itself Rotation of 72 Reflection across the line of symmetry Rotation of 45 None of the above

6 Draw and name the vertical and horizontal cross section for the cylinder below Vertical cross section drawing and name

Question 5 Points 2 Identify the symmetry O Reflection symmetry O Rotational symmetry Both

sson Posttest Points 2 Question 6 Which of the following transformations carry this regular polygon onto itself O rotation of 60 clockwise Orotation of 45 clockwise Orotation of 75 clockwise the line symmetry

Lesson Question 8 Points 2 How many lines of symmetry does a regular octagon have O 4 O 8 O 6

1 In the diagram below a cylinder with a height of 8 yds and a radius of 13 yds 13 yd Determine the surface area a In terms of T the nearest tenth 8 yd

Lesson Posttest Question 1 Points 1 Polygon is a segments joined together closed line O open line O closed curved open curved Polygon onto plane figure made up of

t A gallon of paint will cover approximately 450 square feet An artist wants to paint all the outside surfaces of a cube measuring 12 feet on each edge What is the least number of gallons of paint he must buy to paint the cube 1 1 2 2 3 3 4 4

5 6 7 8 3 1 4 2 In the given picture there are transversal What is the relationship between angles 2 and 6 vertical supplementary corresponding alternate interior alternate exterior Which angle is alternate exterior to angle 8 Just ente the number If angle 5 has a measure of 140 degrees what is the measure of angle 3 CO

n Postte Points 2 Question 2 A point D 3 2 is rotated clockwise through 90 Find the new coordinates of D O D 2 3 O D 2 3 OD 2 3 OD 2 3

n Posttest Question 8 Points 1 Which of the following shows the coordinates of Q 3 5 after a translation of 3 units right O Q 0 5 O Q 6 5 O Q 6 2 O Q 3 2

Question 9 Which of the following shows the coordinates of C if the given rectangle is translated 2 units upward 8 7 6 5 Y 0 D A Y Points 1 2 O 4 3 3 O 3 4 O 4 5 6 5 C B 4 5 6 7 8 X

Question 5 Points 2 Which of the following transformations creates a figure that is similar but not congruent to the original figure O Reflection O Translation O Rotation O Dilation

Question 1 Points 3 The vertices of the triangle are A 3 5 B 6 1 and C 5 9 is dilated using a scale factor 2 Find the coordinates of the dilated triangle O A 5 7 B 8 3 and C 7 11 O A 6 10 B 12 2 and C 10 18 O A 1 3 B 4 1 and C 3 7 O A 6 10 B 12 2 and C 10 18

This table shows how many sophomores and juniors attended two school events A student is selected randomly from this group O A 0 51 OB 0 60 C 0 40 Sophomore Junior Total D 0 26 Jazz band Volleyball concert game 35 42 36 71 24 66 What is the probability that the student attended the jazz concert given that the student is a junior Round your answer to two decimal places Total 77 60 137

5 Given ABCD is a parallelogram Prove 4ABD 4CDB D A C B

Which statement is not always true about a parallelogram a The diagonals are congruent b The opposite sides are congruent c The opposite angles are congruent d The opposite sides are parallel

4 Find the length of TS T 2x 15 S R x 15 U

1 The following polygon is a parallelogram Find the value of x 2x 20 3x 10

2 The following polygon is a parallelogram Find the value of x 8X 6 98

3 Find the mZKSO In the diagram below of parallelogram ROCK m C is 70 and m ROS is 65 TTT R O 65 LYSO3 S C 70 K

Frolls thoushds 9 A bag contains 2 red marbles 7 blue marbles and 8 green marbles If two marbles are drawn out of the bag replacing the first marble before drawing the second marble what is the exact probability that both marbles drawn will be blue 10 A bag contains 8 red marbles 3 blue marbles and 7 green marbles If three marbles are drawn out of the bag what is the probability to the nearest 1000th that all three marbles drawn will be red 11 A bag contains green and yellow color tiles You pick two tiles at random without replacing the fir one The probability that the first tile is yellow is The probability of drawing two yellow tiles is

1 61 16 With replacement 1 Suppose you draw two tennis balls at random from a bag containing 7 pink 4 white 3 yellow and 2 green tennis balls What is the probability of getting yellow replacing the ball and then getting pink Totalt 7 4 3 2 16 Plyellow 3 0 188 16 Unol P pink 7 6 438 16 Without replacement 3 Suppose you draw two tennis balls at random from a bag containing 7 pink 4 white 3 yellow and 2 green tennis balls What is the probability of getting yellow and then green P vellow the Pink 0 188 0 938 0 082 P yellow 0188 P green 7 5 0 133 Mixed Practice 5 A bag contains 6 red marbles 4 blue marbles and 8 green marbles If three marbles are drawn out of the bag what is the probability to the nearest 10th of a percent that all three marbles drawn will be green roubles 6 4 8 18 0 165 0 133 0 025 First Green 1 8 2 A bag contains red and blue marbles You pick 3 marbles at random replacing each marble between picks What is the probability that the last marble you choose is blue if there are 9 red marbles and 6 blue marbles Second 77 our Total marbles 9 6 15 P last is blue 0 4 15 4 A bag contains red and blue marbles You pick 2 marbles at random placing them in a box What is the probability that you get two red marbles if there are 10 red marbles and 8 blue marbles marbles 10 5 1 P first d 10 0 556 18 P secondared 9 0 529 PETRed 0 55610 529 0 294 17 6 What is the probability that you choose a Queen and then a King when choosing two cards from a deck Round your answer to the nearest thousandths place Cards 52 3 2 52 King is 2 1 queen is 0 006

In circle O AE and FC are diameters Arc ED measures 17 A B C What is the measure of EFC O 107 O 180 253 O 270

Triangle BCD is isosceles and BC BD B A 100 What is the measure of BC O 100 O 120 O 130 O 160

F R to 50 H In the diagram of circle R mZFGH is 50 What is mFEH O 130 O 230 260 310 O O

dar Unen 3 Find the equation of x 2y 4 and passes t ver the ques 5 Find the equation of a line that has a y intercept of 2 and it is perpendicular to a line that passes through the points 2 5 and 1 4

4 1 Name Teacher Hailey Complementary supplements Name the relationship complementary pnear par veral orang ngruent 2 9 X 10 e Weds A 8 Score Date 4 5 6 L 1 vertical 9 1 3 Math sids Com

1 Find the area of the figure below 4 4 in 3 7 in 10 8 in A B C D 39 96 in 36 99 in 2 63 99 in 2 93 69 in 2 2 Find the area of the figure below 22 m 2 A 313 80 mm B 308 31 mm C 830 13 mm D 380 13 mm 2

4 Find the missing angle PIS 4 max m n n m x 72 MLZ 44 122 X 8 105 le 2 moure in each diagram 7 MAX may 301 K 950 mza m b MLC m d m e 10 30 E mar MAS m Lt d 2 S 1320 t

Match the z score table to the direction the z scores are read Table entry O Z Choose Choose

Note The height of the triangular face equals 1 73 mm 2 mm 7 mm 2 mm 2 mm Find the surface area to the nearest tenth Select one O a 45 5 mm O b 48 9 mm O c 42 0 mm O d 15 2 mm Find the volume to the nearest tenth Select one a 24 2 mm

Most Costco parking lots average 3 designated van accessible spaces Based on the 1 6 ADA ratio how many parking spaces in the lot are designated as simply accessible

The volume of two similar prisms are 891 cm and 33 cm The surface area of the larger prism is 153 cm What is the surface area of the smaller prism Select one O a 9 cm O b 27 cm O c 51 cm O d 17 cm

8 in Sh Find the surface area to the nearest tenth Select one O a 125 7 in O b 402 1 in O c 251 3 in Od 150 8 in Find the volume to the nearest tenth Hint To find the height of the cone use the Pythagorean Theorem with hypoter equal to 8 in and one of the sides equal to 4 in Select one O a 149 8 in 20 This

Receiving claim Adjusting claim Paying claim Total Activities Receiving claim Adjusting claim Paying claim 26 100 Totals 113 100 34 800 S 174 000 15 b Determine the average total process cost per claim payment assuming 5 800 total claims Round to the nearest whole dollar per paid claim 65 c Prepare a table showing the changes in the activity costs as a result of the changes proposed by management If an amount is zero leave the entry box blank Use the minus sign to indicate an additional cost in the last column 20 100 Statewide Insurance Company Changes in the activity costs Activity Cost Prior Activity Cost to Improvement After Improvement Activity Cost Saving

12 cm 8 cm Find the surface area Select one O a 528 cm O b 48 cm O c 192 cm O d 336 cm Find the volume to the nearest tenth Hint To find the height of the pyramid use the Pythagorean Theore hypotenuse equal 8 cm and one of the sides equal to 6 cm Select one a 761 0 cm Ob 384 0 cm