2D Geometry Questions and Answers

Federico just bought a trampoline Which of these could have been an internal factor that influenced Federico s decision A Federico recently read an article in a magazine about trampolines B Everyone else who lives on Federico s block has a trampoline C Federico has so much fun jumping up and down on trampolines D Federico just saw a movie in which the star jumped on a trampoline

4 y x 5 8

Independent Practice Part 1 7 5 y x 3 40 impli D M HA 6 F

A 12 foot ladder leaning on a house makes a 65 angle with the ground To the nearest foot how far up the house does the ladder reach

pot slide is attached to a swing set The slide makes a 65 angle with the swing set What is the height of the top of the slide

Joel has had his dog Buster for 4 years For Joel dog food is most likely what type of purchase O A Minor repurchase OB Major new purchase OC Minor new purchase OD Major repurchase

Violet has developed a new kind of flour tortilla and now she is trying to decide how much to charge for it Which of the 4Ps of marketing is she concerned with at the moment O A Promotion OB Price O C Product D Placement CARMER FESTS gegrianinai Venanci INTA DE

Grocery Drugstores Health Stores Food Stores What was the average number of locations chosen per potential customer A 2 OB 4 OC 2 5 Big Box Stores 15

In 5 Given the preimage and image state the coordinates of each figure and the scale factor of the dilation with center at origin Answer in simplest fraction form 5 12 2 19 A 6 16 14 O M Q N N 10 12 14 16 X M M Scale Factor Scale Factor N O

In 12 13 Where possible mark any congruent angles and show sides proportional Write a Similarity statement and state whether it is by AA SAS SSS 12 13 B O Similarity Statement Reason 6 30 12 Reason D C 30 Similarity Statement E

In 3 4 describe the dilation enlargement or reduction and state the scale factor Solid is preimage 22 cm 16 cm Type of Dilation Scale Factor 4 3 cm Type of Dilation Scale Factor 18 cm

In 8 11 Use the figure in which ABCDE GHJDF Complete each statement 8 ZF 9 ZD 10 GH AB JD EA 1 ED

each proportion round answers to the nearest tenth NIN 2 8

Justify that the triangles are congruent by connecting corresponding vertices of the pre image and image with line segment F E

EGO NOTE For each pair of triangles write a congruence statement Justify your statement by identifying the congruence pattern you used Then justify that the triangles are congruent by connecting corresponding vertices of the pre image and image with line segments Describe the relationship between the line segments 3

4 A F A B C x 2 2x 1 10 12 18 C E 7 D

19 A 10 foot ladder is leaning against a house so that it reaches a window that is 8 feet off the ground What is the angle that the ladder forms with the ground

20 You decide to measure the height of the stadium lights on the Comets football field The angle of elevation from the ground where you are standing is 32 You are standing 15 meters away from the light post How tall is the stadium light post Draw the figure

24 Find the area of the triangle A bh 11 m 407

12 AB B X A m B m T 27 32 T

22 sin 38 cos 0

Matching 8 9 10 sin A cos A tan A A 1 875 B 0 8824 C 0 4706 A 8 17 15 B

A 12 3x 18 9 A If AABC is similar to ADEF determine the measure of ZA B C 16 22 8 33 4x 2 C D 6 F

11 AB AC X m A 11 35 C

7 Multiple Choice Which ratio is equivalent to sin 32 A cos 32 B sin 58 C cos 58 D tan 3

Find the length of RQ 25 S

Which of the following is true O A B O C JW QA JB QK BW KQ JB KA BW KA JW KA

B A E Which statements show that A ABE is similar to A ACD Select TWO that apply LABELC A A B C D C D ZA ZC 90 2C LD LABE ZAEB 4 38 and C 38

P B C Q Who is correct and why are they correct A D N M Justin is correct because only one pair of angles can be proven congruent and only one pair of sides can be proven proportion Justin is correct because only one pair of angles can be proven congruent Patrice is correct due to SAS similarity Patrice is correct due to AA similarity

T 12 W 8 D X A B D 24 16 18 12 V Yes the triangles are similar with a scale factor of No the triangles are similar with a scale factor of of No the triangles are similar with a scale factor of 32 No the triangles are similar with a scale factor of 23

C C Which set of transformations maps A ABC to A DEC and support Omar s thinking A B C A D a rotation of 180 clockwise about point C followed by a dilation with a center of point C and a scale factor of 2 a rotation of 180 clockwise about point C followed by a dilation with a center of point C and a scale factor of 1 1 201 a rotation of 180 counter clockwise about point C followed by a dilation with a center of point C and a scale factor of 3 a rotation of 180 counter clockwise about point C followed by a dilation with a center of point C and a scale factor of

Question 1 Examine the properties listed below Determine which of the following properties are true for all parallelograms Select three that apply A four right angles diagonals bisect each other B C D E opposite sides are congruent opposite angles are congruent diagonals intersect at right angles

72 Figure Rhombus FGHI H Question 10 Read the question and enter your response in the box provided Use the tools and your keyboard to construct your response What is the measure of ZIHJ ZIHJ What is the measure of ZFGH ZFGH

Find the length of the unknown side of the triangle 12 ft 3 ft The length of the unknown side of the triangle is Simplify your answer Type an exact answer using radicals as needed

A 5 B G 0 5 F D E S Question 12 What shapes can help you find the area of the composite figure A Triangle B Oval C Rectangle D Kite E Trapezoid Yes Yes Yes Yes Yes No No No No No

A 8x 9y 9 Figure Parallelogram ABCD B 10y 2 x 9 Question 7 Determine whether the figure is a parallelogram for the given values of the variables x 9 and y 11 Quadrilateral ABCD is a parallelogram

B Figure Parallelogram ABCD 4x 6 in A y 10 in E 6y in C 3x in D Question 6 Read the question and enter your response in the box provided Use the tools a keyboard to construct your response Use Parallelogram ABCD to find each measure AC inches

Examine parallelogram ABCD below 9y 2 A B C B D 8x6 5x 12 D In order to determine the length of each side of the parallelogram which of the following equations would need to be used Select two that a A 5 12 8r 6 180 C 7y 4 9y2 7y 4 180 5 12 8 6 9y2 7y 4

Question 8 Read the question and enter your response in the box provided Use the tools and your keyboard to construct your response Find the measure of ZZ in order for quadrilateral WXYZ to be a parallelogram Z W 6a 10 186 11 9b 2 mZZ 8a 4 Y X

D Which type of shape could quadrilateral ABCD be Select ALL that apply A B C H D square rhombus rectangle parallelogram

Lesson 12 4 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Use the Geometric Mean Theorem and your knowledge of proportions to find the value of x K 16 X 20 12

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

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

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

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 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