2D Geometry Questions and Answers

Your Turn 1 Find DG 24 F 32 C E 40 G Coometry BIN 2 Credit 2 M 10 5 P R L4L Geom

Your Turn Solve for the missing variable angle measure or side length consen 1 Find the value of x You may assume triangle ABC is similar to triangle STU 63 Find the value of y 100 4x 35 9 Use the diagram in which A ABE AACD 3 Find the value of x 2 What must the missing length be for the two figures to be similar 12 14 NA 6 Tot afrayg A 5 6 cm y cm E D 4 cm 3x 14 5 cm 50 B C

Hailey is considering taking out an 8 year loan with monthly payments of 125 at an APR of 4 7 compounded monthly and this equates to a loan of 9985 95 Assuming that Hailey s monthly payment and the APR of the loan remain fixed which of these is a correct statement OA If it were a 6 year loan the amount of the loan that Hailey is considering taking out would be more than 9985 95 B If it were a 10 year loan the amount of the loan that Hailey is considering taking out would be more than 9985 95 C If it were a 12 year loan the amount of the loan that Hailey is considering taking out would be less than 9985 95 OD If it were a 14 year loan the amount of the loan that Hailey is

Chuck can afford a 490 per month car payment and he s interested in either a convertible which costs 28 700 or a sports car which costs 29 200 If he is being offered a 6 year car loan with an APR of 6 compounded monthly which car can Chuck afford A Chuck can afford neither the convertible nor the sports car B Chuck can afford the convertible but not the sports car C Chuck can afford the sports car but not the convertible D Chuck can afford both the convertible and the sports car

Carter can afford a 220 per month car payment If he is being offered a 5 year car loan with an APR of 2 4 compounded monthly what is the value of the most expensive car he can afford OA 13 119 81 O B 13 199 19 OC 12 427 06 D 13 191 95

Larry is considering taking out a loan He estimates that he can afford monthly payments of 265 for 10 years in order to support his loan He finds that with an APR of 5 5 compounded monthly he can take a loan of 24 418 05 Assuming that Larry s monthly payment and the length of the loan remain fixed which of these statements is true about the size of the loan Larry could take if he received a different APR A If the interest rate were 6 6 the amount of the loan that Larry is considering taking out would be more than 24 418 05 B If the interest rate were 5 2 the amount of the loan that Larry is considering taking out would be less than 24 418 05

Wyatt can afford a 1290 per month house loan payment If he is being offered a 30 year house loan with an APR of 7 2 compounded monthly which of these expressions represents the most money he can borrow A A 1290 1 0 006 360 1 0 006 1 0 006 360 B 1290 1 0 006 360 0 006 1 0 006 C 1290 1 0 072 360 0 072 1 0 072 D 1 1 1290 1 0 072 360 1 en

Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the amount of a 15 year loan with an APR of 15 6 compounded monthly that is paid off with monthly payments of 230 A N 180 1 1 3 PV PMT 230 FV 0 P Y 12 C Y 12 PMT END B N 15 1 15 6 PV PMT 230 FV 0 P Y 12 C Y 12 PMT END C N 15 1 1 3 PV PMT 230 FV 0 P Y 12 C Y 12 PMT END D N 180 1 15 6 PV PMT 230 FV 0 P Y 12 C Y 12 PMT END

13 The vertices of quadrilateral ABCD are given as A 0 3 5 B 3 1 17 C 7 3 15 and D 4 1 3 Prove that ABCD is a parallelogram KU 2

In 4 5 describe the dilation and state the scale factor Solid is preimage 4 5 12 cm 3 cm 8 in 6 in 20 in 15 in

Learning Goal Given two figures I can apply the definition of similarity in terms of similarity transformations to decide if the two figures are similar explain the meaning of similarity for triangles Triangle FGH is transformed into similar triangle JKL using the given transformations Lesson Reflection Circle one Lesson 11 2 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint Complete the Lesson Reflection above by circling your current understanding of the Learning Goal below Translate FGH 3 units down and 2 units left followed by a rotation counterclockwise 90 Then followed by a dilation by a scale factor of 2 1 Draw JKL on the coordinate plane given the above information Starting Getting there Got it 2 4 2 YH 0 2 7 LL F 2 G A Translate

Your Turn Use the Properties of Similar Figures to write a proportion or a congruence statement 1 Figure ABCD is similar to figure MNKL Write a proportion that contains BC and KL 3 AXYZ is similar to AXVW Write the congruence statements that must be true 2 ADEF is similar to ASTU Write a proportion that contains ST and SU

are congruent like the proper Your Turn 1 A builder was given a design plan for a triangular roof as shown Explain how he knows that A AED A ACB Then find AB 9 ft 15 ft 6 ft 15 2 Find PQ if possible 0 9 S 12 R

Your Turn til stand sign galvlqA 1 In AJKI m2 40 and m2K 55 In AMNP m M 40 and m P 85 A student concludes that the triangles are not similar Do you agree or disagree Why 2 In the figure AB II DE Prove that A ACB A ECD Use the Statement Reason Bank to help you complete the proof Statements 1 2 3 4 A ACB A ECD Statement Reason Bank Reasons 1 Given 2 Vertical Angles are Congruent 3 Alternate Interior Angles are Congruent 4 21 24 AB DE AA Triangle Similarity Theorem 22 23 A D Wig 2 3 B

300 00 W two that apply 2 75 7189 611 7 6 ates a figure getting bigger Select 3 What is the scale factor that dilates AWXV to AW X V Ay dilation indicates a figure getting smaller Select two that apply 0 4 1 5 3 15 5 8 4 What is the scale factor that dilates quadrilateral TUVW to quadrilateral T U V W

metry B Similarity Credit Goals Transform mathematical objects to establish relationships through properties and laws Use appropriate tools to make mathematical concepts more concrete and visible Credit 2 ENGAGE Dilation Complete the following activity with your teacher in order to start your learning on similar figures Match the following images with the appropriate transformation i Reflection ii Rotation iii Translation A BB B CN IN 8 In all transformations what is special about the shape and size of the pre image and image S D nother type of transformation is called a dilation Dilations have different properties than the rest of the ansformations In this credit you will learn more about dilations

5 What is the scale factor that dilates quadrilateral HIJK to quadrilateral H I J K H 6 What is the scale factor that dilates quadrilateral HIJK to quadrilateral H I J K H Optional Complete problems 2 5 12 13 15 17 from your textbook on separate lined paper for extra practice When you are finished check the odd problem for solutions at the back of the textbook

Learning Goal Given a center and scale factor I can verify that dilating a figure leaves any lines passing through the center of the figure unchanged takes a line not passing through the figure s center to a parallel line makes dilations of line segments longer or shorter in the ratio given by the scale factor Starting Getting there Lesson 11 1 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoin below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 The dilation from ALMN to triangle AL M N has a scale factor of Write the coordinates for L M N and the graph both the pre image and the image L 3 3 M 3 6 N 3 3 L M N 2 4 2 0 2 4 ty 2 4

3 Square A is a dilation of square B What is the scale factor Show your thinking A B Explanation 35

B In 9 10 Write a similarity statement and state the similarity ratio 10 H I 20 Similarity Statement Similarity Ratio 15 K 18 00 OP 30 15 M NO Q 25 Similarity Statement Similarity Ratio

15 16 Where possible mark any congruent angles and show sides proportional Write a Similarity statement and state whether it is by AA SAS SSS 16 15 Similarity Stmt Reason M A B D 6 Reason 4 5 Similarity Stmt F E

Use JDRT JHYX Complete each statement 11 ZD 12 ZY 13 JD JH DR 14 RT YX JX D 11

8 AABC has vertices A 8 4 B 14 16 and C 6 10 What are the vertices of the image after a dilation 1 with a scale factor of using the origin as the center of dilation 4

In 17 18 the figures are similar setup a proportion then find the value of the variable Round answer to the nearest tenth 17 X 12 10 6 18 15 X 12 9

Solve each proportion round answers to the nearest tenth 5 r 12 2 7 8 x 3 3 ilarity x 8 x 1 4

Which graph is used to model piece rate pay O A Scatterplot OB Quadratic equation OC Piecewise OD Piece rate PONEKA C De

Owen is an hourly employee and the line that models his total pay in dollars as it relates to the number of hours he has worked has a slope of 25 and a y intercept of 15 Which statement is true O A Owen s wage is 25 an hour but it appears that he received no signing bonus OB Owen s wage is 15 an hour and it appears that he received a signing bonus of 25 OC Owen s wage is 25 an hour and it appears that he received a signing bonus of 15 D Owen s wage is 15 an hour but it appears that he received no signing bonus

When modeling hourly pay which part of the equation is used to represent the total pay O A X O B y intercept O C y D None of the above

10 5 O A 5 OB 11 O C 10 O D 1 2 3 4 5 X

A B b Dilation of 2 about the point 5 2 Center to 4 How man A B 2 A 8 6 ER 6 8 y Center to B C C D Center to C D Center to b Dilation of 3 about the point 1 2 G H F Center to 10 11 12 G H F Center to

A B C Date Per A Describe the following dilations with enlarge or reduce the scale factor and the center of dilation 2 3 Center to A C 2 A B C D Center to D E F Center to E E F 1 Center to 2 R F E P Q R Center to P R Center to L T 10 T

C Solve the following Proportions Leave all answers as a simplified fraction and as a decimal rounded to the tenths 1 8 24 12 X 5 2 12 20 X 15 3 x 2 8 2 3

H 25 A X D AC BC AD BD BC BD LBAC 25 LACD X X P

Consider the following Which of the following shows a different way to tessellate the shape in the figure above Select all that apply

Use triangles to find the sum of the interior angle measures of each polygon a 60 b 60 x

Find the value of x for each parallelogram a 48

Find the value of x for the rectangle X x 3 b 24 x 8 c 6 3x X 9 3

b Oright trapezoid c isosceles trapezoid kite parallelogram rectangle rhombus d square isosceles trapezoid 000 kite parallelogram rectangle rhombus right trapezoid square isosceles trapezoid kite parallelogram rectangle rhombus right trapezoid square isosceles trapezoid kite parallelogram rectangle rhombus right trapezoid square

An angle that has a measure between 0 and 180 corresponds to a reflex angle that has a measure between 180 and 360 The interior reflex angles of the polygon below are congruent The interior acute angles are also congruent The measure of each interior reflex angle is 252 Find the measure of each interior acute angle

Ava is 35 years old She has 1000 in a checking account 7500 in Investments 15 000 in a retirement account and owns a house worth 30 000 What is the total value of her liquid assets OA 23 500 OB 53 500 OC 8500 OD 38 500

Which describes the difference between a property s market value and the amount that is currently owed on the property OA Capital gain OB Net worth C Owner s equity

The number of a country s unemployed workers decreased from 5 3 million to 3 9 million last year If the country s population remained constant at 75 million how did its unemployment rate change last year OA It decreased by about 18 OB It increased by about 18 C It increased by about 2 D It decreased by about 2

What is the median of the following string of values 16 95 3 37 97 13 27 42 64 14 OA 32 OB 42 OC 37 OD 27

Ichiro took out a subsidized student loan of 13 000 at a 3 6 APR compounded monthly to pay for his last two semesters of college If he will begin paying off the loan in 15 months how much will he owe when he begins making payments OA 13 000 00 since the government is responsible for the interest on the loan that accrues before Ichiro starts making payments B 13 597 45 since Ichiro is responsible for the interest on the loan that accrues before he starts making payments OC 13 000 00 since Ichiro is responsible for the interest on the loan that accrues before he starts making payments D 13 597 45 since the government is responsible for the interest on

Alondra took out a car loan for 22 500 that has a 0 APR for the first 2 months and will be paid off with monthly payments over 5 years For ho many months will Alondra be charged interest OA 24 months B 36 months C 84 months D 60 months

Homer took out a 6 month loan for 700 at an appliance store to be paid back with monthly payments at a 20 4 APR compounded monthly If the loan offers no payments for the first 3 months which of these groups of values plugged into the TVM Solver of a graphing calculator will give him the correct answer for the amount of the monthly payment over the last 3 months of the loan A N 3 1 20 4 PV 736 31 PMT FV 0 P Y 12 C Y 12 PMT END B N 3 1 20 4 PV 700 PMT FV 0 P Y 12 C Y 12 PMT END C N 0 25 1 20 4 PV 700 PMT FV 0 P Y 12 C Y 12 PMT END

Lulu took out a 3 year loan for 1800 at an electronics store to be paid back with monthly payments at a 15 6 APR compounded monthly If the loan offers no payments for the first 8 months how much will Lulu owe when she begins making payments OA 1995 94 OB 2865 58 C 2584 26 OD 1800 00

Nell took out a subsidized student loan of 6000 at a 4 8 APR compounded monthly to pay for her last semester of college If she will begin paying off the loan in 10 months with monthly payments lasting for 20 years what will be the total amount that she pays in interest on the loan OA 3345 60 OB 9345 60 OC 9724 80 OD 3724 80

5 3 Quiz Luella took out an unsubsidized student loan of 37 00 compounded monthly to pay for her last six semesters of college If she begin paying off the loan in 33 months with monthly payments lasting for 20 years what will be the amount of her monthly payment OA 273 92 OB 240 11 O C 271 56 D 238 04

A cylinder is a polyhedron with circular bases A True OB False