2D Geometry Questions and Answers

1 Determine a plane motion which will take AABC to AA B C B A B

5 0 OR ANALYSIS Describe the error in finding m C A 55 5 B 6 sin C sin 55 6 5 6 sin 55 5 sin C m C79 4 he Law of Cosines should have been used he lengths of the sides in the denominators should be switc ross multiplication should have been used to obtain the solu he inverse sine function should have been used to obtain th

Consult the figure To find the length of the span of a proposed ski lift from A to B a surveyor measures the angle DAB to be 25 and then walks off a distance of L 1900 feet to C and measures the angle ACB to be 15 What is the distance from A to B eccos The distance from A to B is approximately feet Do not round until the final answer Then round to two decimal places as needed GEZER B D 25 A

10 The area of a circle is 244 cm Determine the length of the diameter to the nearest whole number

12 In the diagram below of circle 0 mABC 260 What is mLABC Label it on the diagram below A C 0 B

13 In the circle C below mzBCA x 12 and mAB 3x 24 What is the m AFB a 15 b 30 c 48 B A antwollol odsto C E F

11 5 20 4x 5 85 40 Solve for x

From Lesson 9 06 Probability Two Way Tables The two way table shows the medal count for the top performing countries in the 2012 Summer Olympics Silver Bronze 29 29 27 23 26 32 17 19 99 103 United States China Russia Great Britain Total Gold 46 38 24 29 137 Which statement is true The probability that a randomly selected silver medal was awarded to Great Britain is 17 99 Total 104 88 82 65 339 The probability that a randomly selected gold medal was awarded to China is 88 137 TH The probability that a randomly selected medal won by Russia was a bronze medal is ability that or furthe United St cib dalis 104

A fast food restaurant kept information about the drinks that were ordered along with the different sized kids meals as shown in the table Milk Regular Kids Meal Large Kids Meal Total 55 71 Juice Box 22 60 Soda 63 86 Total 156 280 Which statements are true Select three options Milk was requested for 16 of the large sized meal orders Sixty three of the orders of soda came with a regular sized meal Soda was requested for 280 of the kids meal orders

From Lesson 9 05 Conditional Probability Lori downloaded all the pictures she took at Rita s wedding into a single computer folder She took 86 of the 134 pictures with her camera and the remainder of them with her cell phone Of the pictures Lori took with her cell phone one out of every five was blurry To the nearest whole percent what is the probability that when she opens a random picture from the computer folder it will be a blurry picture she took with her cell phone 7 13 31

From Lesson 9 05 Conditional Probability Use the Venn diagram to calculate probabilities P A A 15 16 31 P A B 2 1 1 P B 6 Which probability is correct B 10 4 U

Under the best conditions a sprout has a 40 probability of blooming If two sprouts are selected at random what is the probability that both will bloom under the best conditions 16 24 40

In a standard deck of cards there are four suits spades clubs hearts and diamonds Each suit has one each of 13 cards ace king queen jack 2 3 4 5 6 7 8 9 and 10 If event A is choosing a king event B is choosing a heart and event C is choosing a jack which Venn diagram could represent this description C B 2 B B

Farid is at a music festival where several bands play at the same time There are 5 bands playing from 3 00 to 4 00 and 3 bands playing from 4 00 to 5 00 From 5 00 to 6 00 2 bands are playing Lastly there are 7 bands are playing from 6 00 to 7 00 Assuming Farid goes to see exactly one band every hour how many different sets of bands can Farid see at the music festival ways

Three out of seven students in the cafeteria line are chosen to answer survey questions How many different combinations of three students are possible 7C3 7 35 70 7 7 3 131

What are the corresponding parts of the figure L 37 in 32 N 100 49 in 26 in 48 M

From Lesson 9 02 Finding Outcomes Fiona chooses three towels from a group of five to pack in her beach bag for herself and her two brothers Let th five towels be represented by A B C D and E If Fiona chooses towel A for herself which statements about the possible outcomes for her brothers towels are true Select three options There are 10 possible ways to choose the group of towels The combination BC is not the same as CB She has four choices for the first brother s towel and three choices for the second brother s towel ABC ABD ABE ACD ACE and ADE are the possible outcomes If Fiona did not choose towel A for herself there would be more outcomes

From Lesson 9 02 Finding Outcomes Holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on the side of the ho If order does not matter in how many ways can she choose the plants for the front of the house 7 9 21

From Lesson 9 01 Sets and Venn Diagrams The Venn diagram shows the number of patients seen at a pediatrician s office in one week for colds C ear infections E and allergies A U 10 16 28 44 15 3 How many patients total were seen for only a cold only an ear infection and only allergies

From Lesson 9 01 Sets and Venn Diagrams The universal set is the set of rational numbers S is the set of integers Which represents Sc xlx is a real number xlx is a rational number mber

What are the corresponding parts of the fig L 17 m 108 12 m K M 98 121 39 m 41 m 34

Jon an aspiring meteorologist spent the past few weekends studying the clouds He took detailed notes on the types of clouds observed and the time of day they were observed Morning Afternoon Evening Stratocumulus 6 4 2 Stratus 4 3 3 What is the probability that a randomly selected cloud was marked as stratus or was not observed in the afternoon Simplify any fractions

Number 1 From Lesson 9 01 Sets and Venn Diagrams U C x B Which statements are true about x Select three options xeBUC XEBNC XEAUC XEANC XFA

Amelia works at a coffee shop on weekends Every now and then a customer will order a hot tea and ask Amelia to surprise them with the flavor The teas are categorized by flavor and caffeine level Caffeine free Caffeinated Mint Fruity Chai 3 5 7 8 4 4 What is the probability that a randomly selected tea is fruity or is not caffeine free Simplify any fractions

A skating rink attendant monitored the number of injuries at the rink over the past year He tracked the ages of those injured and the kinds of skates worn during injury In line skates Roller skates Minors Adults Seniors 3 3 3 4 4 5 What is the probability that a randomly selected injured skater was an adult or was not wearing roller skates Simplify any fractions

After growing tired of squinting while driving Felix went shopping for a pair of sunglasses He tried on glasses with different frames and lenses Polarized lenses Regular lenses Cat eye frames Browline frames Aviator frames 2 4 12 11 7 What is the probability that a randomly selected pair of sunglasses has aviator frames or browline frames Simplify any fractions

6 What is the length of the bolded arc 18 5 ft b 72 6 ft 9 2 ft d 36 3 ft a C el ssdw 21 36km bus 24x 30A ON 14 5 ft 73 to to svecesib sii

What are the corresponding parts 19 mm 43 0

The owner of a sushi restaurant looked over some recent orders He noted how many yellowtail and salmon rolls had been ordered Yellowtail Salmon Not spicy Spicy 2 4 2 3 What is the probability that a randomly selected sushi roll contains yellowtail and is not spicy Simplify any fractions

7 In circle K above the area of sector JKL 94 in Determine m JKL to the nearest tenth of a degree A 94 in SPA K 14 ic

Determine the measure of arc DGF 75 105 210 50 KED REVIEW 7 4x D H 8x 31 E F

1 Which of the following is a radius A QT B PS C QS D QP 2 Which of the following is a diameter A QT B PS C QS D QP 3 Which of the following is a chord that is not a diameter A QT B PS C QS D QP P Q R T

Which rule explains why these triangles S P Q 11 T

What are the corresponding parts of the figu P 40 21 m 115 26 m 108 970 Q 8 m

Dalton is shopping for a new bicycle He is most interested in color and type of tires Red Green Road bike tires Mountain bike tires 5 4 6 5 What is the probability that a randomly selected bike is green or has road bike tires Simplify any fractions

3 In the diagram above of circle 0 m AOC 3x 5 and m ABC x 15 What is the mAC 5 b 20 C 25 d 40 80 a e A B

Kira looked at some boxes of cereal in the grocery store For each one she recorded the size and whether or not it contained a prize Mini size Regular size Prize No prize 3 3 3 1 What is the probability that a randomly selected box of cereal is regular size or contains a prize Simplify any fractions

4 In the circle above mzQ 3x mLU 2x 12 mzA 2x and mzD 2y Detern U

2 Find the value of x K 83 M L 9x 40

a EF b GD C CB d DB intercepts which arc C A D E B LL F INSCR 2

You spin the spinner once 3 1 2 What is P less than 2 Write your answer as a percentage rounded to the nearest t

Alec attended his town s annual Worm Charming Competition Contestants are assigned to a square foot of land where they have 30 minutes to charm worms to the surface of the dirt using a single technique Alec observed contestants charming techniques and kept track of how many worms surfaced 5 10 worms 11 20 worms 21 30 worms Tapping the ground Raking the ground 6 5 5 8 10 4 What the probability that a randomly selected contestant charmed 11 20 worms or 5 10 worms Simplify any fractions

2 Using circle O determine mzPQR and mPR 90 R a mzPQR 90 mPR 90 b mzPQR 180 mPR 90 mzPQR 45 mPR 90 mzPQR 90 mPR 45 radius is 9 cm

2 Use the Zero Product Property to identify the x intercepts Find the y intercept line of symmetry vertex and draw a sketch graph for each function a y x 4x 32 x intercepts y intercept line of symmetry vertex product sum 5 15 20 25 30 35 9 10x

4 Convert the equations to standard form from vertex form then use the Zero Product Property to identify the x intercepts Find the y intercept line of symmetry vertex and draw a sketch graph for each function a y x 5 9 Step 1 Convert to standard form standard form Step 2 Factor standard form and use Zero Product Property to find x intercepts product sum 10 5 Step 3 Use the information below to graph x intercepts y intercept line of symmetry vertex

trapezoid rhombus or kite shown below 36 in b 7ft c 19 ft 9m 21 ft 14 ft 45 m 24 In A A

8 Find the indicated measure a Find the radius of a circle with an area of 153 94 square millimeters r b The area of a circle is 12 57 square miles Find the diameter of the circle

5 Regular pentagon ABCDE is inscribed in circle G B a FG is a n A apothem B radius side of the pentagon b CD is a n A apothem B radius side of the pentagon 6 What is the area of the shaded region 5 in 10 in 4 in 3 in 7 in 6 in 15 in A 10 in

A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers The consulting company gathered data from each customer who purchased hiking shoes and recorded the shoe brand and the customer s level of happiness Displeased Pleased A Footlong shoe A Toes Knows shoe 3 3 3 3 What is the probability that a randomly selected customer is pleased or purchased a Toes Knows shoe Simplify any fractions TELEP C O 2 55

7 Find the area of the regular polygon 32 cm