Geometry Questions

Learning Goal from Lesson 11 2 and 11 3 Given two figures I can apply the definition of similarity in terms of similarity transformations to OB DC decide if the two figures are similar explain the meaning of similarity for triangles 3 Choose a sequence of similarity transformations that maps AABC to ADEF Lesson 11 2 1 point A A reflection across the x axis and a scale factor of 2 A reflection across the y axis and a scale factor of 2 A reflection across the x axis and a scale factor of 0 5 b List an angle that is congruent to ZD 12 8 D c List a side that is proportional to DE How I Did Circle one I got it A 4 E B 8 ty 0 8 C I m still learning it F 4 4 Polygons BCDE and FGHI are similar You will have to draw your own quadrilateral to solve this problem Lesson 11 3 2 points a Write a proportion that contains BC and FI X

2 AABC was dilated to create AA B C 1 point What is the scale factor of the dilation lifelong EARNIND Geometry B Credit 2 8 L A 8 ty M 8 C A C 8 8 y B LAL Geometry B 2020 8 8 Page

Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the same value for PV as the expression 355 1 0 002 1 0 002 1 0 002 36 OA N 3 1 2 4 PV PMT 355 FV 0 P Y 12 C Y 12 PMT END B N 3 1 0 2 PV PMT 355 FV 0 P Y 12 C Y 12 PMT END C N 36 1 0 2 PV PMT 355 FV 0 P Y 12 C Y 12 PMT END D N 36 1 2 4 PV PMT 355 FV 0 P Y 12 C Y 12 PMT END

esson 11 2 Homework HW Complete problems 1 4 below for independent practice 1 Which one of the following best describes the 2 Which combination of transformations below dilation of XYZ to X Y Z below best describes the change from ABC to WXY A OB When you are finished check the solutions with your teacher Z AA scale factor of 2 about the center BA scale factor of 0 5 about the center CA translation of x 3 y 1 D A rotation of 90 clockwise 3 Which combination of transformations below best describes change from KLMN to GHIJ C A rotation A rotation 90 clockwise and a scale factor of 3 A rotation 270 ciockwise and a scale factor of 3 90 counterclockwise and a scale factor of 0 SE B A A translation 2 5 units up and 3 units right dilated by a scale factor of 2 A translation 2 5 units down and 3 units left dilated by a scale factor of C None of the above OB 2 4 Which combination of transformations below best describes the change from ABC to EDC B OC A A reflection across the x axis and a scale factor of 2 A reflection across the y axis and a scale factor of 2 A reflection across the y axis and a scale factor of C E Optional Complete problems 1 3 6 8 18 19 from your textbook on separate lined paper for extra practice

The following group of values was entered into the TVM Solver of a graphin calculator N 108 1 6 6 PV PMT 620 FV 0 P Y 12 C Y 12 PMT END Which of these expressions will return the same value for PV A B 1 108 620 1 0 0055 0 0055 1 0 0055 108 620 1 0 066 108 1 0 066 1 0 066 108 O C 620 1 0 0055 1 0 0055 1 0 0055 D 620 1 0 066 1 LAS CCC

1 Liam is 6 feet tall To find the height of a tree he measures his shadow and the tree s shadow The measurements of the two shadows are shown Find the height h of the tree Liam 3 6 ft 8 ft Tree A 28 ft

Find the geometric mean of the numbers If necessary give the answer in simplest 1 6 and 24 2 5 and 12

Camilla entered the following group of values into the TVM Solver of her graphing calculator N 24 1 1 2 PV PMT 480 FV 0 P Y 12 C Y 12 PMT END Which of these problems could she be trying to solve A A person can afford a 480 per month loan payment If she is being offered a 2 year loan with an APR of 1 2 compounded monthly what is the most money that she can borrow B A person can afford a 480 per month loan payment If she is being offered a 24 year loan with an APR of 14 4 compounded monthly what is the most money that she can borrow OC A person can afford a 480 per month loan payment If she is being offered a 2 year loan with an APR of 14 4 compounded monthly what is the most money that she can borrow

1 A student wanted to find the height h of a statue of a pineapple in Nambour Australia She measured the pineapple s shadow and her own shadow The student s height is 5 feet 4 inches What is the heigh of the pineapple Remember 1 foot 12 inches 8 10 2 ft CE 8 ft 9 in F

R HW 143 12 3 Homework 1 If AFGH ATSR find the value of GH H 3x 20 104 S 3 If AWVT ARST find the value of VT W T 104 G 8 66 Complete problems 1 6 below for independent practice 39 32 When you are finished check the solutions with your teacher 5 AEFG AEKL are similar Solve for x 30 14 ent Practice R 2 If AFGH ATUH find the value of HT 84 H dan 45 4 AKLM AKCD are similar Solve for x 63 108 8 M 4 K K 28 6 AKLM AKQP are similar Solve for x 2x 8 16 D 3x 1 zod Optional Complete problems 2 4 6 7 11 17 18 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions

8 to TUVW Map ABCD to EFGH DE PD Map A ABC to A DEF W T 0 8 6 2 6 63 D 2 2 4 H 4 6 S 6 8 ormation to confirm the figures are similar There is one extra option A You can map by a reflection across the y axis followed by a dilation of 8 B You can map by a reflection across the x axis followed by a dilation of 2 C You can map by a rotation about the origin 180 followed by a dilation of 1 5 followed by a translation 3 units to the right and 1 5 units up D You can map by a reflection across the y axis followed by 2 units to the left and 4 units down

1 To find the distance d across a stream Levi located points as shown in the figure Use the given information to find d lifelong B 12 m C E 6 m 12 m D

1 Verify that TU and RS are parallel A 72 11 90 67 5 U 54 S

S 35 C 56 e B HW H 1 Find the missing length The triangles in each pair are similar 30 3 Find the missing length The triangles in each pair are similar 10 C 7 84 5 e B 36 P C S CB QR Solve for BR Then using that value solve for SR K Complete problems 1 6 below for independent practice A R R ework 33 S When you are finished check the solutions with your teacher Figures are not drawn to scale You can assume that all segments that appear to be parallel are indeed parallel 2 Find the missing length The triangles in each pair are similar K R 2 K N 10 24 10 42 4 TS I LK Solve for LT Then using that value solve for TJ 70 P S 6 NM AB Solve for AN Then using that value solve for AC 70 20 16 70 M 40 Optional Comple problems 6 7 verify that the given pair of segments are parallel 11 15 16 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the textbook

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

Travis is considering taking out a 20 year loan with monthly payments of 380 at an APR of 1 4 compounded monthly and this equates to a loan of 79 504 54 Assuming that the APR and the length of the loan remain fixed which of these is a correct statement OA If Travis s monthly payment were 350 the amount of the loan that he is considering taking out would be less than 79 504 54 OB If Travis s monthly payment were 310 the amount of the loan that he is considering taking out would be more than 79 504 54 O C If Travis s monthly payment were 330 the amount of the loan that he is considering taking out would be more than 79 504 54 D If Travis s monthly payment were 420 the amount of the loan that

Triangle Similarity Theorem S 67 V 67 U 3 What should ZD and ZC be to make these two triangles similar E W 92 41 F Triangle L M 45 N 48 40 P 4 What should ZF and Z be to make these two triangles similar H 55 Q F

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 1 Your friend incorrectly claims that A ABC is similar to A FGH by SAS Similarity Triangle Theorem Explain or show your friend their misunderstanding of SAS Similarity Theorem NA 10 9 H B

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

HW 3 Complete problems 1 4 b 1 Are the two figures similar If they are solve for 2 Are the two figures similar If they are solve for the missing the missing side 49 70 AV 3 The two figures are similar AABC transforms into ADFE What is the scale factor E 14 7 When you are finished check the solutions with your teacher B 6 D 26 24 25 D 4 The two figures are similar QRST transforms into LMNO What is the scale factor 3 40 R L 16 10 Lea

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

Determine the scale factor that dilated the pre image to its image 1 Figure ABCD to A B C D Scale Factor 2 Figure EFGHI to E F G H T Scale Factor B E B A A 6 4 2 Ty 4 2 0 F E F C O Y D 2 O D 4 G H X 6 G L M H

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

2 Your Turn Is this transformation a dilation 1 Determine if the transformation on the coordinate plane is a dilation The scale factor is done for you Preserves angle measure Y N Preserves orientation Y N Scale Factor Is this transformation a dilation Preserves angle measure Y N Preserves orientation Y N Scale Factor Yes Is this transformation a dilation 16 J J D 4 N 0 A aya B n E B 00 U B 421 12 2 0 A T

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

7 Quadrilateral MATH has vertices M 6 4 A 4 2 T 0 1 H 1 8 What are the vertices of the image 5 after a dilation with a scale factor of using the origin as the center of dilation 2

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

A quality assurance specialist makes 22 an hour for the first 40 hours she works during a week and 29 an hour for each hour worked over 40 hours Which piecewise equation models her total weekly pay y in dollars as it relates to the number of hours x that she has worked during the week 22x A y 129x OB y C y 22x 29 x 40 22x 29x 880 0 x 40 x 40 0 x 40 X 40 0 x 40 x 40

2 SEE O A Hourly pay with no bonus OB O C Piece rate Exakt 3 Commission pay D D Hourly pay with a bonus X 4

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