2D Geometry Questions and Answers

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

What is the cross section that is parallel to the base of a sphere triangle oval parabola circle Question 8 1 point What is the shape of the cross section of a regular square pyramid if the cross section is parallel to the base Triangle Circle Rectangle Square

states and applies Cavalieri s Principle These stacks of coins have the same volume because each cross section has the same area and they have the same height A cone and cylinder will have the same volume if they have the same base area and the same height These two stacks of coins have the same volume because they have the same height

A cone is the result of rotating which of the following shape triangle rectangle pentagon circle

A 15 meter by 25 meter plot of land has 120 trees on it What is the population density of the trees 0 32 tree per meter 2 3 125 trees per meter 2 120 trees per meter 2 375 trees per meter 2

2 In right triangle ABC shown below altitude AD is drawn to hypotenuse AC DB 5 and BC 20 What is the length of the altitude in simplest radical form B D

6 In the given diagram determine the sum of a and b Tisda St BOVI od 21 Jailw woled 38A signsho in griz S 15 a b 30

2 Using right triangle ABC below what is the value of AC BC to the nearest wh triang a 9 6 b 15 c 6 plest radical form d 5 C 52 B 12

4 Which of the following statements are true given the two right triangles bel apply a sinB cosA b cosE sinE c sinE cosD d cosB sinA SIMILARITY 2012 E B 0 10 B What is the length SR D 6 8 Study com

8 In right triangle ABC mzC 90 CA CB and BA 12 Determine the length of CA