Geometry Questions

6 cos x 3 0 x 2 Type an exact answer using as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the express

Scale Factor 11 1 Center Point N M O IM N

Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19 angle of elevation from the ground How high will the ramp rise from the ground at its highest end Round your answer to the nearest tenth of an inch if necessary

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

opposite sides are congruent opposite angles are congruent the diagonals of a parallelogram bisect each other Standard G CO 11 EXPLORE Read the section below and complete the following activity adapted from Lesson 9 1 A quadrilateral is a polygon with four sides A parallelogram is a quadrilateral that has two pairs of parallel sides L4L Math Resources http bit ly L4LMath Proving the Opposite Sides Criterion for a Parallelogram Draw and explain in your own words the following polygons Make sure to use tick marks to label congruent sides and arrows to label parallel sides Definition of a Quadrilateral Definition of a Parallelogram

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

Glenda lives in Ohio which has a sales tax of 5 5 She just bought a grill whose full price was 220 but she got 40 off because the store was having a sale What was the total amount that Glenda paid OA 139 26 OB 88 00 OC 92 84 OD 132 00

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

EXPLAIN 1 Proving Opposite Sides Are Congruent Read the section below and complete the following activity adapted from Lesson 9 1 A segment that connects two nonconsecutive vertices of a polygon is a diagonal 6 Theorem 1 If a quadrilateral is a parallelogram then its opposite sides are congruent Example reason box at the bottom of page Prove that the opposite sides of a parallelogram are congruent Answers given in statement Given ABCD is a parallelogram Prove AB CD and AD CB The figure WXYZ is a parallelogram WZ XY and WX ZY Statements 3 AB DC AD BC 4 ZADB ZCBD LABD LCDB 5 DB DB 1 ABCD is a parallelogram 2 Draw DB 7 AB CD and AD CB Statement Reason Bank 3 1 2 Through any two points there is exactly one line 4 D 5 Reasons 6 ASA Triangle Congruence Theorem 7 4 Alternate Interior 1 Given Angles Theorem 5 Reflexive Property of Congruence 7 CPCTC This number tells you the correct row number in the proof for each statement or reason provided below 3 Definition of parallelogram 6 A ABDA CDB 0

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

EXPLAIN 2 Proving Opposite Angles Are Congruent Read the section below and complete the following activity adapted from Lesson 9 1 Example Prove that the opposite angles of a parallelogram are congruent Given ABCD is a parallelogram Prove ZA ZC A similar proof shows that ZB ZD 5 Theorem 2 If a quadrilateral is a parallelogram then its opposite angles are congruent The gure WXYZ is a parallelogram 2ZWX 2XYZ and ZWZY ZWXY 1 ABCD is a parallelogram 2 Draw DB 6 3 AB DC AD BC 4 7 Statements Statement Reason Bank 1 2 6 3 1 Given D Reasons 4 Alternate Interior Angles Theorem 5 Reflexive Property of Congruence 6 ASA Triangle Congruence Theorem 7 A ABD A CDB 2 Through any two 7R CPCTC points there is exactly one line W 7S LA LC B 4 LADB LCBD LABD LCDB 5 DB DB 3 Definition of parallelogram

Leon lives in North Dakota which has a sales tax of 5 He jus home theater system whose full price was 450 but after sending in a rebate form he later received a check in the mail for 75 What was the total amount that Leon ended up paying after receiving the rebate OA 393 75 OB 397 50 O C 472 50 D 375 00

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

Your Turn 1 According to Theorem 1 label the parallelogram with the appropriate tick marks I If a quadrilateral is a I parallelogram then If a quadrilateral is a parallelogram then B 2 According to Theorem 2 label the parallelogram with the appropriate tick marks If a quadrilateral is a parallelogram then B Tick marks show congruency 3 According to Theorem 3 label the parallelogram with the appropriate tick marks B Tick marks show congruency Use the Glossary if you come across any unknown words

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

The minimum monthly payment for Fern s credit card is 2 5 of her balance or 40 whichever is higher If Fern s balance at the end of her last billing cycle was 1950 what is her minimum monthly payment OA 48 75 OB 40 00 C 88 75 OD 8 75

13 ASRT ACBD S 70 T 11 x 4 R D 50 B 60 C 14 I 72 J 27 4 4x U L 36 96

Chloe filed for Chapter 13 bankruptcy in 2008 Even if she planned to take the maximum time allowed under Chapter 13 to repay her debts she must have planned to repay them by no later than what year OA 2016 OB 2015 OC 2013 OD 2014

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

Cindy lives in Connecticut and makes 59 000 a year If the median annual income is 68 595 in Connecticut and 50 233 in the United States as a whole is Cindy likely to qualify for Chapter 7 bankruptcy A No Cindy is not likely to qualify because her yearly income is below the median annual income of Connecticut O B Yes Cindy is likely to qualify because her yearly income is above the median annual income of the United States as a whole C Yes Cindy is likely to qualify because her yearly income is below the median annual income of Connecticut OD No Cindy is not likely to qualify because her yearly income is above the median annual income of the United States as a whole

4 M 30 30 D 130 20 N Similarity Stmt Reason 5 R X Similarity Stmt Reason B 6 B X Vi C Z Similarity Stmt Reason

In 1 6 Mark any congruent angles and show sides proportional Then write a Similarity statement and state whether it is by AA SAS SSS 1 A B 3 O R Similarity Stmt Reason 2 9 P M A 12 15 20 16 Similarity Stmt Reason 12 W P 8 4 Similarity Stmt Reason M 2 A B

Which type of bankruptcy is available to all businesses but I corporations to put a stay on creditors while allowing the company to reorganize with the company sometimes continuing to run or being put up for sale while it is bankrupt O A Chapter 7 OB Chapter 9 O C Chapter 11 OD Chapter 13

Jose s only debt obligations are a car loan payment of 436 and a credit card payment of 50 every month What is the minimum amount of money he must take home every month in order to avoid being in danger of credit overload OA 1944 OB 2180 O C 2430 D 486

Shelby s annual take home pay is 51 000 What is the maximum amount that she can spend per month paying off credit cards and loans and not be in danger of credit overload O A 4250 00 OB 850 00 O C 1062 50 OD 3400 00

6 61 A C 5

The Vaughns make 58 000 a year and live in Florida which has a median annual income of 47 778 If their monthly expenses amount to 4600 per month do they qualify for Chapter 7 bankruptcy OA Yes the Vaughns qualify because their yearly income is above the median annual income of Florida The means test is irrelevant in this case B Yes the Vaughns qualify because their yearly income is above the median annual income of Florida They are eligible according to the means test O C C No the Vaughns do not qualify because their yearly income is above the median annual income of Florida They are ineligible according to the means test

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

Which of these debts could possibly be forgiven under Chapter 7 bankruptcy OA A student loan OB A mortgage O C Child support O D Alimony

XYZ Insurance offers an annuity with 5 9 APR for the next ten years You decide to invest 100 each quarter into this account What type of annuity is this OA Recurring payment fixed annuity OB Single payment variable annuity C Recurring payment variable annuity D Single payment fixed annuity

Danielle invests 50 a month in an annuity that earns 4 APR and is compounded monthly What is the future value of Danielle s account in 3 years O A 1909 06 OB 2082 39 OC 2153 85 D 1843 29

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

Bao is trying to find the height of a radio antenna on the roof of a local building She stands at a horizontal distance of 27 meters from the building The angle of elevation from her eyes to the roof point A is 34 and the angle of elevation from her eyes to the top of the antenna point B is 37 If her eyes are 1 7 meters from the ground find the height of the antenna the distance from point A to point B Round your answer to the nearest tenth of a meter if necessary

Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19 angle of elevation from the ground How high will the ramp rise from the ground at its highest end Round your answer to the nearest tenth of an inch if necessary

Find the exact value of cos A in simplest radical form B 7 85

Solve for 2 Round to the nearest tenth if necessary X 64 70 H

Find the exact value of cos A in simplest radical form 7 B C 6 85 A

Find the exact value of tan C in simplest form 3 B C V21 V30

Solve for 2 Round to the nearest tenth if necessary X OB 6 7 P