2D Geometry Questions and Answers

What is the value of x A 84 140 04x C ONLY TYPE THE NUMERICAL VALUE

c A 210 O 35 60 mm B Find the length of the arc AB in terms of O 70 T O 220 T O 2100 T

What is the measure of the angle x x A 80 B ONLY TYPE THE NUMERICAL VALUE

2 Kiran is flying a kite He gets tired so he stakes the kite into the ground The kite is on a string that is 18 feet long and makes a 30 degree angle with the ground How high is the kite 18 30 3 Triangle ABC has a right angle at C Select all measurements which would mean it has a hypotenuse with a length of 10 units A Angle A is 20 degrees BC is 2 units B AC is 7 units BC is 3 units C Angle B is 50 degrees BC is 4 units D Angle A is 30 degrees BC is 5 units E AC is 8 units BC is 6 units B A

Find the value of a and b Angle XQR is 180 1 2 3 5 X 7a 135 107 5b 87 la 91 16 20 M 11a 174 121 4b M lb 91 4a 117 M 40 5b 75 L R 77 4a 91 101 R R 102 3a X 3a 134 109 5b 222 11a 118 5b 9a 185 4b 84 98 3a 142 3a LS 91 3b Ko 2b 48 149 5a M M M 70 3b R R

Scale Factor 11 1 Center Point N M O IM N

bestion Given E is the midpoint of AC complete the flowchart proof below Given E is the midpoint of AC Given AE EC Rea Given ZB ZD Reason AABE ACDE Reason ZBEA ZCED Vertical angles are congrumt Rea

Annette has a credit card that uses the previous balance method The opening balance of one of her 30 day billing cycles was 2990 but that was her balance for only the first 7 days of the billing cycle because she then paid off her entire balance and didn t make any new purchases If her credit card s APR is 31 which of these expressions could be used to calculate the amount Annette was charged in interest for the billing cycle OA 9 307 50 365 OB 30 0 31 365 O C 0 31 365 50 23 2990 30 2990 23 50 30 30 0

Loretta lives in Virginia which has a sales tax of 4 She just bought a pair of binoculars whose full price was 280 but she presented the retailer with a coupon for 60 which the retailer accepted What was the total amount that Loretta paid O A 291 20 O B 231 20 OC 228 80 OD 220 00

Shawna lives in Alaska and makes 66 500 a year If the median annual income is 68 460 in Alaska and 50 233 in the United States as a whole is Shawna likely to qualify for Chapter 7 bankruptcy A No Shawna is not likely to qualify because her yearly income is below the median annual income of Alaska B Yes Shawna is likely to qualify because her yearly income is above the median annual income of the United States as a whole C No Shawna is not likely to qualify because her yearly income is above the median annual income of the United States as a whole D Yes Shawna is likely to qualify because her yearly income is helow the median annual income of Alaska

Use the rhombus VWXY from Example 3 to find each measure 1 m2VYX 2 mZXYZ Y 6m 12 9n 4 Z X W 4m 4 3n 0 75

Lesson 9 1 Homework HW T Complete problems 1 5 below for independent practice 1 Solve for x in the parallelogram below 18x 7 When you are finished check the solutions with your teacher U 65 V 7x 5 5 8x 5 3 Solve for x in the parallelogram below Then find the measure of ZY 2 Solve for x in the parallelogram below Then find the measure of QR P A The perimeter of ABCD is 2AB 2BC B DE DB C BC DC D ZDAC ZBCA E AAED ACEB F ZDAC ZBAC S x 2 O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No R 6x 6 4 Solve for x in the parallelogram below Then find the measure of 2T U 2r 2 9x 21 0 V 5 ABCD is a parallelogram Determine whether each statement must be true Select the correct answer for each lettered part W D Optional Complete problems 6 7 10 13 17 18 24 from your textbook on separate lined paper or extra practice When you are finished check the odd problems for solutions at the back of the textbook B

Since JKLM is a rhombus JM By the Reflexive Property of Congruence JNN so AJNM AJNK by the So by CPCTC By the Linear Pair Theorem ZJNM and JNK are supplementary This means that m JNM m JNK Since the angles are congruent m JNM m JNK so by m JNK m JNK 180 or 2m JNK 180 Therefore m JNK Statement Reason Bank 1 Because JKLM is also a parallelogram MNKN because 8 and JK JMK 4 4JNM JNK 3 SSS Triangle Congruence Theorem 2 Diagonals of a 5 parallelogram bisect each other 6 180 Substitution 7 90

four Turn 1 Draw and explain in your own words the following 2 According to the properties of rhombuses label the rhombuses below appropriately 1 I I I Definition of a Rhombus Properties of Rhombuses If a quadrilateral is a rhombus then If a parallelogram is a rhombus then If a parallelogram is a rhombus then I I I I

Proving Diagonals Bisect Each Other Read the section below and complete the following activity adapted from Lesson 9 1 Theorem 3 If a quadrilateral is a parallelogram then its diagonals bisect each other The figure WXYZ is a parallelogram WY XZ Below is the flow proof that the diagonals of a parallelogram bisect each other Given ABCD is a parallelogram Prove AE CE and BE DE AB DC Definition of parallelogram ZABEZCDE Alternate Interior Angles Theorem ABCD is a parallelogram Given ZBAEZDCE Alternate Interior Angles Theorem D AB DC Opposite sides of a parallelogram are congruent AABE ACDE ASA Triangle Congruence Theorem 8 AE CE and BE DE CPCTC

4 Justify Reasoning Determine whether each statement is always sometimes or never true You may draw a picture of each situation to help you Explain your reasoning The first one is done for you If quadrilateral RSTU is a parallelogram then RS ST Sometimes opposite sides of a parallelogram are congruent but consecutive sides may or may not be congruent If a parallelogram has a 30 angle then it also has a 150 angle If quadrilateral GHJK is a parallelogram then GH is congruent to JK In parallelogram ABCD ZA is acute and ZC is obtuse In parallelogram MNPQ the diagonals MP and NQ meet at R with MR 7 cm and RP 5 cm

Your Turn 1 Solve for x in the parallelogram below 4 PR 16 6x 2 PQRS is a parallelogram Find each measure 3 QR 2 Solve for x in the parallelogram below 17x 4 E 72 B 2z 4 S P x 9 T 4x 6 R 3z 4

find each measure using the rectangle below to help you 2 AD 7 5 cm and DC 10 cm Find DB 3 AB 17 cm and BC 12 75 cm Find DB If you know two sides of a right triangle you can find the third side using Pythagorean Theorem a b c a C b

Properties Two pairs of opposite sides are Il Two pairs of opposite sides are Exactly 1 pair of opposite sides are II Exactly 1 pair of opposite sides are All sides are Two pairs of adjacent sides are Two pairs of opposite Zs are Exactly 1 pair of opposite zs are All zs are Each pair of base Zs are Diagonals are jagonals are L onals bisect each other The Sides The Angles The Diagonals the Isosceles Trapezoid

According to the properties of rectangles label each rectangle with the appropriate tick marks Properties of Rectangles A 1 I I If a quadrilateral is a rectangle then If a parallelogram is a rectangle then D A D B B

In 7 14 Set up a proportion then find the value of x Round to nearest tenth 7 9 8 11 X 5 J D 6 X 15 8 10 12 9 12 7 4 X

17 Graph the lines Two triangles should be formed Label the coordinates of their vertices 4 points m 8 y 4 8 x 4 Poin 4x 2y 4 12 2x 2 y x 2 Slope 6 2 y 8 8 x 3 m 8 Point 3 8 1 b 2 10 4 4 10 314 10 e 0 2 18 Identify a triangle congruence theorem that proves the triangles above are congruent Use words and calculations to justify your answer 10 6 points

10 8 12 17 X 15 10 11 3 8 X 12 42 12 X

24 B bones C 9 16 A

Jocelyn takes home 2600 per month from her job as a paralegal If her only debt obligations are a car loan payment of 480 and a credit card payment of 80 every month is she in danger of credit overload A No because the sum of 480 and 80 is less than 650 B Yes because the sum of 480 and 80 is less than 650 C No because the sum of 480 and 80 is greater than 520 OD Yes because the sum of 480 and 80 is greater than 520

What is the name of the fee charged by a financial institution for withdrawing money from an account before the maturity date OA Early redemption fee OB Surrender charge C Liquidity fee

Suppose a triangle has sides 1 1 and 1 Which of the following must be true OA The triangle in question may or may not be a right triangle B The triangle in question is a right triangle C The triangle in question is not a right triangle

What is the approximate volume of a tree trunk if the trunk is 12 feet tall with a circumference of 4 5 feet Recall that the circumference of a circle is equal to pi times its diameter OA 25 92 ft3 OB 21 17 ft3 O C 19 34 ft O D 29 40 ft3

Laura has a 1000 bond with a 3 4 coupon Laura purchased this bond for 1065 What is the yield of this new bond OA 3 0 O B 3 6 OC 3 4 OD 3 2

Harry took out a 25 year loan for 160 000 at 9 6 interest compounded monthly If his monthly payment on the loan is 1409 05 how much of his first payment went toward note reduction OA 129 05 OB 1280 00 OC 1409 05 OD 135 27

Find EF in the trapezoid EF A E B 2 D 2x 5 5x 4 F

Which two solid figures have the same volume A A cone with a base of 5 cm and a height of 10 cm B An oblique solid with a base of 5 cm and a slant height of 10 C An oblique prism with a base of 5 cm and a height of 10 cm D A rectangular solid with a base of 5 cm and a height of 10

Which will have a higher effective interest rate a payday loan for 2500 due in 17 days with a fee of 130 or a payday loan for 2500 due in 15 days with a fee of 130 OA A payday loan for 2500 due in 15 days with a fee of 130 because it has the shorter period O B A payday loan for 2500 due in 17 days with a fee of 130 because it has the longer period O C A payday loan for 2500 due in 15 days with a fee of 130 because it has the longer period D A payday loan for 2500 due in 17 days with a fee of 130 because it has the shorter period

Find the measures of the numbered angles in the kite m21 Type an integer or a decimal m22 Type an integer or a decimal The figure is not drawn to sc

Buffy is considering taking out a 14 year loan with monthly payments of 165 at an APR of 2 3 compounded monthly and this equates to a loan of 23 680 66 Assuming that Buffy s monthly payment and the length of the loan remain fixed which of these is a correct statement OA If the interest rate were 2 5 the amount of the loan that Buffy is considering would be more than 23 680 66 OB the interest rate were 2 7 the amount of the loan that Buffy is considering would be more than 23 680 66 OC If the interest rate were 2 1 the amount of the loan that Buffy is considering would be less than 23 680 66 O D If the interest rate were 2 9 the amount of the loan that Ruffy is

Which of these is an optional deduction for money to be taken out of an employee s paycheck OA Social Security OB Medicare OC Disability insurance OD Federal income tax

Which of these is an example of a recurring payment variable annuity A An annuity with an APR of 3 4 into which you invest 2500 each year B An annuity with a minimum APR of 3 4 into which you invest 2500 each year C An annuity with an APR of 3 4 into which you invest a lump sum of 12 500 D An annuity with a minimum APR of 3 4 into which you invest a lump sum of 12 500

A tax on which of these products or services would not be Cax O A Clothing OB Alcohol O C Tobacco D Gambling

If a company has 5 employees with annual salaries of 40 000 50 000 40 000 60 000 and 90 000 what is the mean annual salary at the company OA 56 000 OB 70 000 OC 50 000 OD 40 000

Fruit cocktail comes in large and small cylindrical cans The larger can has a radius and height that are both twice as long as that of the radius and height of the smaller can If the volume of the smaller can is 28 64 in3 what is the volume of the larger can A 229 12 in OB 57 28 in 3 C 114 56 in OD 171 84 in

Given a sphere with a diameter of 6 2 cm find its volume to the nearest whole number A 125 cm B 998 cm3 OC 70 cm D 39 cm

The diameter of a soccer ball is 8 65 inches What is the volume of the ball rounded to the nearest hundredth OA 338 88 in OB 313 42 in3 OC 323 18 in OD 234 06 in

In triangle ABC mZA 45 mZB 40 and a 7 Which equation should you solve to find b OA sin45 7 OB B Cos45 sin40 b co840 b C sin45 b D b272 2 7 bcos40 sin40

The ratio opposite describes which function adjacent O A Tangent OB Cosine OC Secant OD Sine

Last year a construction worker had a gross income of 29 700 of which he contributed 7 to his 401 k plan If he got paid monthly how much was deducted from each paycheck for his 401 k plan OA 173 25 OB 86 63 C 39 98 D 297 00

Suppose a triangle has two sides of length 32 and 35 and that the angle between these two sides is 120 Which equation should you solve to find the length of the third side of the triangle A c 32 35 2 32 35 cos120 B c 322 352 2 32 35 sin120 sin32 120 D 322 352 2 32 35 cos120 C sin35 b

Gertrude accepted a job as a fashion model after being offered a 375 signing bonus If she makes 56 an hour which equation models Gertrude s total pay y in dollars as it relates to the number of hours x that she works OA y 56x 375 B y 56x 375 OC y 375x 56 D y 375x 56

O A square O B rectangle OC circle OD oval

3 Name the major arcs in OO containing point F Select all the major arcs by their correct names k E

5 Consider the graph shown y 2 0 2 Sp 100 150 200 250 300 350 n a Determine the equation of a sine function that matches the graph going function that matches the gra