2D Geometry Questions and Answers

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

10 cm Find the surface area to the nearest tenth Select one O a 1256 6 cm O b 3141 6 cm O c 418 9 cm Find the volume to the nearest tenth Select one O a 4188 8 cm Ob 418 9 cm c 12566 4 cm

2 AF AD LF ZD Triangle AFE and triangle ADE 3 ZROQ ZPQO R E 0 13 1 13 1 10

The circumference of a standard baseball is about 9 in About how many square in of horsehide are required to cover 100 balls to the nearest whole number Select one O a 25447 in O b 2578 in O c 821 in O d 900 in

For problems 5 and 6 use the figure below 2 in 7 in 2 in Find the surface area Select one O a 64 in 2 O b 32 in 2 O c 84 in 2 O d 28 in 2

A food company makes regular and tall soup cans The area of the base of both cans is 30 cm The volume of the regular can is 270 cm The tall can is 2 cm taller What is the volume of the tall soup can Select one O a 330 cm O b 540 cm O c 295 cm O d 300 cm

Is the average time to complete an obstacle course when a patch is placed over the left eye Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye The completion times are shown below Left means the patch was placed over the left eye and Right means the patch was placed over the right eye Time to Complete the Course Right 43 41 40 46 42 40 49 50 Left 44 44 40 49 43 40 48 53 Assume a Normal distribution What can be concluded at the the a 0 05 level of significance level of significance For this study we should use Select an answer a The null and alternative Ho Select an answer H Select an answer hypotheses would be Select an answer Select an answer C please enter a decimal Select an answer Please enter a decimal Select an answer b The test statistic c The p value d The p value is a e Based on this we should Select an answer the null hypothesis f Thus the final conclusion is that please show your answer to 3 decimal places Please show your answer to 4 decimal places The results are statistically insignificant at a 0 05 so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye The results are statistically significant at a 0 05 so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye The results are statistically significant at a 0 05 so there is sufficient evidence to conclude that the eight volunteers that were completed the course faster on average with the patch over the right eye compared to the left eye The results are statistically insignificant at a 0 05 so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye

G 14 00016 N 8 79 D 2 3 over P C A 7 6 5 4 3 2 11 1 2 3 4 5 6 7 X fas B How do the areas of the parallelograms compare O The area of parallelogram ABCD is 4 square units greater than the area of parallelogram EFGH O The area of parallelogram ABCD is 2 square units greater than the area of parallelogram EFGH O The area of parallelogram ABCD is equal to the area of parallelogram EFGH O The area of parallelogram ABCD is 2 square units less than the area of parallelogram EFGH

There are approximately 17 620 people per square mile in New York City If New York City is 468 square miles approximately how many people live in New York City

The density of gold is 19 3 grams per cm What is the mass of a gold block in grams that measures 10 cm by 3 cm by 3 cm