2D Geometry Questions and Answers

ow do we prove that two triangles are congruent In other words what is true about two congruent triangle Given AD bisects BE BE bisects AD AB DE ZA ZD Prove AABC ADEC B

Jessie does a lot of traveling for business When he travels he likes to run to stay in shape He has noticed that the amount of time he is able to keep running impacts the maximum distance he can run and also that the elevation of the city he s visiting impacts how long he is able to keep running Max distance Jessic can run miles 5 4 3 2 0 10 Max time Jessie can run min 30 40 50 20 50 40 30 20 10 Max time Jessie can run min timo Jessic 1000 2000 3000 Elevation feet 4000 a If Jessie is visiting a city with an elevation of 4000 feet how long is he able to keep running minutes 5000 b Based on your answer to part a what is the maximum distance Jessie can run in that city miles c If Jessie is visiting a city with an elevation of 0 feet what is the maximum distance Jessie can run in that city miles d If Jessie is visiting a city with an elevation of 5200 feet what is the maximum distance Jessie can run in that city

Area of Composite Figures Find the area of each figure Round to the nearest tenth if necessary 1 6m 10 m 6 ft 5 ft 4 ft 3 ft 2 12 yd 12 yd 6 cm 5 cm 3 3 5cm 5 cm 7 cm 4 in 6 cm h 14 cm 3 5 cm 9 in 5 in 6in 6 in 10 cm 18 in 4 in 10 in 8 in

9 10 11 12 13 14 Study Year 0 1 2 3 4 5 6 7 8 refer to the following information Artic Sea Ice Extent million km 5 98 6 18 6 08 5 59 5 95 4 32 4 73 5 39 4 81 4 22 3 63 5 35 5 29 4 68 4 72 Extent million km 76547 0 a 0 The predicted decrease in extent in millions of square kilometers of Arctic sea ice per year during the period predicted extent in millions of square meters of Arctic sea ice at the end of the nd The function a defined by a t c dt where c and d are constants models the extent in millions of square kilometers of Artic sea ice t years after the start of he study during a period in which the change is pproximately linear What does d represent The predicted total decrease in extent in millions of square kilometers of Arctic sea ice during the period 1 he predicted extent in millions of square ometers of Arctic sea ice at the beginning of period 2 Arctic Sea Ice Extent Over Time 3 6 7 8 9 10 Year A team of research climatologists conducted a 14 year study to determin the change in the area of the Arctic sea covered with ice termed the Ar sea ice extent The graph and table above model the extent a in million square kilometers of Arctic sea ice t years after the study began yer 12 4 5 13 destiny u To date LO 11 12 13 14 am 08 T CATOR ORSIN The rate of decrease of Artic sea ice extent from 7 to Year 10 is nearly constant On this interva of the following best models the extent a in m of square kilometers of Arctic sea ice t years study began A a 5 0 21t B a 7 0 13t C a 10 0 64t D a 15 1 82t Over which time period is the average Arctic sea ice extent the greatest A Year 4 to Year 5 B Year 7 to Year 8 C Year 9 to Year 10 D Year 12 to Year 13

Questions 17 19 refer to the following information box width w 17 box height h total height Note Figure not drawn to scale When designing stacked displays of different types of crackers for sale a manufacturer can use the box size formula h 3w 30 where h is the height of each box of crackers in inches and w is the width of each box of crackers in inches For any given stacked display the height and width of each box displayed is the same The height of each level in the stacked display is equal to the height of the boxes of crackers in the display For example there are 2 levels in the figure above each with a height of h The total height of the stacked display is the sum of each level s height as shown in the figure Some cracker manufacturing companies require that for wheat crackers the box height must be at least 12 inches and the box width must be at least 3 inches According to the box size formula which of the following inequalities represents the set of all possible values for the box width that meets this size quirement 06 w 12 3 w 6 18 A manufacturer wants to use the box size formula to design a stacked display that has a total height of 7 feet holds boxes with a height between 8 and 10 inches and contains an even number of levels With the manufacturer s constraints which of the following must be the width in inches of the box 1 foot 12 inches A 6 8 B 7 2 8 4 19 C D 10 Which of the following expresses the box width terms of the box height A w 30 30 h 30 30 h B W w C w 30 h D w 30 30 h

2014 is trigine so 7c 5d 10 ULLT For the solution c d to the system of equatio above what is the value of c d C A B 14 U 5 7 5 6 5

Year which lions er the 15 A B C D W following is equal to the ratio 62 Triangle WXY is shown above Which of the WZ WX N N N N XZ XY XY XZ X XZ YZ Z 28 Y

An office supply vendor that delivers printer ink to companies charges a subscription fee of 230 for its services plus x dollars for each carton of ink If a company paid 1 364 for 18 cartons of ink including the subscription fee what is the value of x A 46 B 52 C 63 D 78

The board of directors at a natural history museum decided to survey all of its scientists to determine if the new wing in the museum should feature an aquatic exhibit The board met with a sample group of 30 marine biologists The majority of the sample group were in favor of featuring an aquatic exhibit in the new wing Which of the following is true about the board s survey A The sample group should have included more marine biologists B It concludes that a majority of the scientists are in favor of featuring an aquatic exhibit in the new wing C The sample group is biased because it is not representative of all scientists D The sample group should have consisted only of scientists who are not marine biologists

B C A 7 16 9 16 7 50 16 50 An animal shelter held an adoption event to find new homes for a group of dogs and cats The table above shows the number and color of dogs and cats that were adopted at the event Each animal was classified as only one color Of the cats that were adopted what fraction were black Color Brown Black Species Dogs 13 21 Cats 9 7

Corporate Cable Speedy Connections Global Networks Dave s Dial Up Other Percent of Households 47 21 17 12 3 The table above summarizes a census of 2 800 households within a small community Based on the table how many households receive their Internet service from either Corporate Cable or Global Networks A 1 792 B 1 843 C 1 904

3 Temperature F 40 30 20 10 y 2 Farhart Block A 4 6 8 Time minutes Block B I 10 12 The graph above shows the temperature of two different blocks of metal that are being cooled in a freezer to a temperature of 0 degrees Fahrenheit Both blocks lose heat at a constant rate and Block B started at a lower initial temperature to decrease the time required to cool it Block A took 8 minutes to cool to 0 degrees Fahrenheit and Block B took 12 minutes to cool to 0 degrees Fahrenheit According to the graph what was the difference in degrees Fahrenheit between the initial temperatures of Block A and Block B A 10 B 15 C 20 D 25

16a 20b 12 J Which of the following inequalities is equivalent to the inequality above UT LAUTAS 156 A 5b 4a 4 T 5a 4b 3 B C a b 4 D 4a 5b 3

at right and label the Copy the triangles missing side lengths 30 60 45 45

6 In rectangle ABCD above AC 26 and AD 24 What is the m BAC A 22 6 B 42 7 C 47 3 D 67 4 A D B

7 In right triangle RQW above approximately what is the value of RQ WQ Figure is not drawn to scale A 3 B 8 C 9 D 12 S 2589 vasar R 70 3 15 53 enameldon se W

In the diagram above AABC and ADEF are right triangles where the m B 90 and the mZE 90 Which of the following is not true A sin A cos C B sin D cos F C cos D sin F D cos A sin D A 43 3 B In right triangle SRT below the m R 90 the mZS 30 and SR 4 what is the length of ST 8 3 3 16 3 5 B C 3 D 16 12 EN A bass 3kavade 3 E LO R 5 Sass A F

0 The angle of elevation from a rock on the ground to the top of a tree is 38 If the rock is 20 feet from the base of the tree grid in the height of the tree to the nearest tenth Ignore units when gridding your answer

1 In right triangle ABC the mC 90 CA CB and CA 3 Determine the length of BA A 1 B V 3 2 C 2 D 6 av n

8 If the mzC 90 What is the order of sides from smallest to largest Figure not drawn to scale A AC AB CB B CB AC AB C AC CB AB D AB CB AC 1200 rad ois A rock C A 5 49 7 a

Directions For questions 11 12 solve each problem in the space provided and box your fina any available space in your test booklet for scratch work 11 4 points In the diagram above of AADB where angle B is a right angle Determine the length of DC to the nearest whole number D X 15 45

12 4 points In AABC m CBA 90 m CAB 60 and AB 3 3 a 2 points Find the length of CB in simplest radical form b 2 points Find the length of CA in simplest radical form Ac

What is the percent by mass of K CO3 in a solution if 7 6 grams K CO3 is dissolved in enough water to make 609 g of solution Your Answer

A solution contains 3 7 grams of salt per liter How many liters of the solution would contain 27 grams of salt Round your answer to two decimal places Show your work here

A 0 340L solution of AlBr3 has a molarity of 2 36M How many grams of AlBr3 were used to make this aqueous solution Your Answer

You are building a ramp that must cover a horizontal distance of exactly 9 feet The angle of the ramp from the ground is 21 Determine the length of the ramp in feet Round to two decimal places as needed Show your work here

F x 8 G 144 E 1210 1 A x 26 1340 B 180 S D 900 107 C A 540 27 540 8 548 540 3

your path 40 A brother s path c 60 ft Your younger brother has challenged you to a swimming race to see who can swim to the opposite side of the pool first You know that your brother swims more slowly than you so to make things more even you choose to swim along a path at a 40 degree angle from the path that would go directly across the pool as shown in the diagram The pool is 60 feet wide Activate Windo

3 Given 3 nonlinear points A B and C construct with compass and straight edge a circle contain ing them Given the three nonlinear points A B and C below construct a circle that contains them all A

by the govem In right theo right triangle BAC MLA 90 BC 14 cm and BA 16 cm Determine AC in simplest radical form

Using the figure to the right find the measure of the radius r 11 8 5 S 577 181 O A 0 r S

ORX 2 40 light numbers 10 20 2 tyd hog A number from 1 72 is chosen at random Find decimal and percent P multiple of 9 Hidedang antal P factor of 72 and even 8 72 11 111

Initial Knowledge Check Question 8 The shorter leg of a right triangle is 6 inches shorter than the longer leg The hypotenuse is 6 inches longer than the longer leg Find the side lengths of the triangle

Find the measure of the indicated arc L 65 K 120 1300

Solve for the indicated Arc 30 T U S V 60 K 123

Find the outer perimeter 18 ft 14 ft D 10 ft Remember Co 2 r I P ft Round to the nearest hundredth Use 3 14 for Enter

8 Solve for the indicated angle D E 68 Z 136

Solve for the measure of angle Z X 42 F Y 99 100 104 Z

ATSU ATKJ K Match the image with the congruence statement 4 S K S U

11 R K L statement with the approp AJKL APLR R P K 11 R P K J 11 L R 1

Find the measure of angle RSQ 150 Q 130 R 80 65

K UT X T Match the image with the con K T K

Not enough information H Determine if the two triangles are congruent If they are state you know SAS AAS SSA HL

VUT AVFG F U G T U Match the image with the congruence statement G T F U G T F U

AAA 1 HL Determine if the two triangles are congruent If they are state how you know 2 SSS 3 SAS Not enough information 5

What is the shape of the cross section of a regular square pyramid if the cross section is parallel to the base Circle Square Rectangle Triangle Question 5 1 point What is the cross section of a cylinder parallel to the base ellipse circle rectangle triangle

P 50 in UTG S Which of the following statement about cylinders P and S is TRUE If x y the volume of cylinder P is equal to the volume of Cylinder S because the cylinders are the same height If x y the volume of cylinder P is less than the volume of cylinder S because cylinder S is slanted If x y the area of a horizontal cross section of Cylinder P is greater than the area of a horizontal cross section of Cylinder S If x y the area of a horizontal cross section of Cylinder P is equal to the area of a horizontal cross section of Cylinder S ha

find the volume of the cone 8cm 6cm 366 7 cm 301 59 cm 364 4 cm 386 5 cm Question 13 1 point

Two stacks of 23 quarters each are shown One stack forms a cylinder but the other stack does not form a cylinder Stack 1 Stack 2 Why are the volumes of these two stacks of quarters equal Use Cavalieri s Principle to explain your thinking Every cross section perpendicular to the bases has an equal area Because both stacks have height the stacks must have the same volume If Stack 1 was twisted it would look like Stack 2 so the stacks must have the same volume If Stack 2 was straightened it would look like Stack 1 so the stacks must have the same volume Every cross section parallel to the bases has an equal area Because the stacks are the same height the stacks must have the same volume

Which is the resulting 3D figure from rotating the 2D shape below about the horizontal axis 2 E