2D Geometry Questions and Answers

MA 912 GR 1 5 Directions Complete the formative assessment in the space provided below b1tb2 2 MS Workspace Tulips should be planted three inches apart to give a full look The Starlings have a trapezoidal plot for a flower garden as shown in the figure They are going to tulips along the parallel sides of the garden The midsegment to the garden is 10 feet long Tulips are sold in bags of 25 bulbs x 4 ft 10 x x 4 x x 4 2 10 Part A What are the lengths of the parallel sides of the garden Part B How many tulips are needed to line the parallel sides Part C What is the minimum number of bags the Starlings need to purchase to have enough bulbs to line the parallel sides of the garden Part A Find CD Quadrilateral ABCD is a kite Part B Find the perimeter of kite ABCD A 12 5 8 T D MAS

1 Explain why ANRT ANPM 8 R 11 A 5 For 5 7 complete the following proportions X 6 X H M 12 N 8 T N MJ For 8 12 find the following variables 3 M 30 G S 9 For 2 4 complete the follo 5 For 11 12 find the following variables GN GM NH R W 12 2 T 7 6 2 X 3 4 GJ GH GN SV SR RT 18 ST SW SV 10 AA a 9 SR VW TR 7 GM NHMJ

Day 5 Use the figure to complete the proportions 1 3 EF BA FG 5 C X 4 EB FA FG n D H 9 18 Determine the value of the variable so that DE BC A 15 2 X 4 E X 6 riangles Segment Lengths CB BA EF Determine the length of each segment 7 FE 8 AF EG AY ED CB Find the value of the variable 21 B 30 A 6 4 cm G 4 cm 10 B B 3 cm H E 25 K A B 6 cm L 4 20 6 18 D 21 C 8 B 5 cm M 8 NY P D

The 19 explain why it is segments in each figure are tangent to the circle at the points shown Find each length A 20 B 21 D 5r 7 7r 9 Co B A n 8 Co B 2n 8 D 22 Co Co A A B 11z 7M 14z 2 8c 1 10c 15 D D

Which step s will map ABCD onto A B C D B A TG D AY B A C D OA Translation 8 units left and 4 units down OB 180 clockwise rotation about the origin C Translation 8 units left and reflection over the x axis OD Translation 8 units right and 4 units up

Level ML 6 Add subtract multiply and divide polynomials 5WQ Divide If the polynomial does not divide evenly include the remain 13v117 v 9

Divide If the polynomial does not divide evenly 2 3y 11y 10y y 2 19

neach circle A and B are points of tangency Find the measures of the inscribed ngle and the circumscribed angle 5 12x 1 C A B 4x 5 D 16 4x 6 A D B 6x 14

Using the graph below point B is represented by U

Given the graph below which coordinates represent the point E Select one or more a 3 b 420 3 C 2 3 d 3 4 e 4 3 f 3 420

Given the graph Find a Find the equation Select one or more 1 20 a b c d 10 e f a a 1 20 a 5 a 5 a x a y 6 8 y a x 6 h x a y 5 20 10 0 10

10 Find the exact area of the surface obtained by rotating the curve about the x axis 9x y 18

What is the volume of this figure 4 in 11 in 13 in cubic inches 7 in 4 in

A larger tree is to the left of a smaller tree The smaller tree casts a shadow of 15 feet and is 6 feet tall The larger tree is 20 feet tall and the shadows of both trees meet at the same point Grid in the length of the larger tree s shadow Ignore units when gridding in your answer

Choose the true statements about this conic section x 3 1 4 64 25 1 Select one or more a Opens to the left and right b Center 3 4 c Center 4 3 d The graph opens vertically up and down

AABC AFED and AB 6 in BC 8 in CA 10 in and the perimeter of FED is 36 in Grid in the sum of ED and DF Ignore units when gridding in your answer Gin 10in B 5 8 instal 201 C CASE fe veas lambobs nicido od llw 2010 nom duiw is odysm 11 sib liftszom

In the figure below AE CD and segment AD intersects CE at B creating similar triangles Grid in the length of segment CE sirius 10 B 5 8 E

x 10 3 points The area of ALMN is 200 ft and the area of AXYZ is 1 600 ft The length of LM is Determine the length of XY to the nearest tenth

Identify the cross section of the regular square pyramid Assume objects are perpendicular if they appear so

FO PG diagram above AJ BK CL DM EN AB BC CD DE EF FG GH HI AB 2 and NE mi6 what is the length of JA A 12 B 14 voors C 16 D 18 oul to nousup K 2920 M D A B C D E F G H

Find P Even Number Numbered Card O 59 2 THAT TH 9 19 kr

Find P Red King Face Card 82 38 32 HIT TART THE AUTA AUTA 54 87 29 1 MACE

Dependent An opaque bag contains 5 green marbles 3 blue marbles and 2 red marbles If two consecutive marbles are drawn without replacement what is the probability that the first one will be green and the second one will be red 0 51 0 0 10 OOT 0 16

92 L 68 a What m PN b What m c What m LM M P Figure 3 6 3pts each Using Figure 3 above fil the following PNM N

Question 11 Right triangle RST is shown below with the dimensions given in feet ft A 15 1 B Which is closest to the measure of ZR C 15 7 74 3 S D 74 9 17 ft T 63 ft R

b What m c What m 123 B Figure 1 3 3pts each Using Figure 1 above find the following a What m AC BC AB C

In the following figure line L is parallel to line M and angle 3 is a right angle a Name a pair of alternate interior angles b Name a pair of corresponding angles c Name a pair of non adjacent complementary angles 6 7 1 2 3 5 4 89 M

10 Determine the measure of angle ABC in the figure The dotted lines are all vertical lines Explain your reasoning A B 63 42 C 30

A student determined the measures of the following angles in the order listed but they did not explain their reasoning For each step give a justification that the student could use for why it is the measurement stated In the figure BD is parallel to AE Step 1 Step 2 Step 3 ZBDC 78 ZCDF 102 Zx 102 Justification A C 32 B 70 D F E X

8 In the following figure line AB is parallel to line DE Which pairs of angles are equal Justify your responses Name angles clearly A C B

A circle has the equation x y 3x 4y 4 0 Graph the circle using the center h k and radius r Find the intercepts if any of the graph Use the graphing tool to graph the circle

Find the value of c in rhombus PQRS R Q 4c 8c 12 P S

12 Describe a relationship between the angle 0 the hypotenuse makes with the z axis in each triangle and the angle of rotation Use the diagram to help you think about the question The dotted arc shows the angle of rotation 7 201

Find the value of u in rhombus BCDE C 3u 29 B D 2u E

Find the volume generated when the region bounded by the graphs of y x 2 and y e is rotated around the following axes of revolution 1 y 2 2 y 2 3 x 3 4 x 2

39 Draw the triangle ABC where A 0 0 B 2 0 and C 0 1 The image of ABC is A 0 2 B 0 4 and C 1 2 Find three different ways of trans forming triangle ABC so that after each of e transformations its image is triangle A B C

2 Sketch a graph of the function a x x 4 Describe the transformations to the graph of y x 4143

What value of c makes x 2 24x c a perfect square trinomial 144 48 48 144

The two questions below ask for approximations of the derivative Make sure you show any calculations you use get a Pass give the best approximation for the derivative 1 Approximate f 2 f x 2 3 2 4 1 5 6 1 0 0 5 1 3 4 4 5 5 73 1 1 5 57 7 9 10

Find the equation for the plane through the points Po 4 2 5 Qo 1 1 4 and Ro 0 4 5 The equation of the plane is

Use an identity to write each expression as a single trigonometric function value or as a single number See Example 4 17 cos 15 sin 15 1 20 1 2 sin 22 22 12 2

44 Draw a diagram and find the remaining part of the right triangle If b 48 A 36 c A 35 OB 26 C 82 D 59

Given ZBAC LACD and ZADB ZDBC Prove ABCD is a parallelogram Step 2 Statement ZBAC LACD ZADB ZDBC LBEA ZDEC try Type of Statement A B Reason Given Vertical angles are congruent D

46 Draw a diagram and find the remaining part of the right triangle If a 2 52 c 4 75 A A 58 B 32 O C 28 D 62

Find the rectangular coordinates of the point 9 150 The rectangular coordinates of the point are Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

operties of parallelograms Parallelogram 4 5 perpendicular congruent complementary 1 point bisect supplementary Consecutive same side angles are Answer bisect complementary congruent perpendicular 1 point supplementary Diagonal bisectors are Answer

9 Find EF C F 7x 39 Type your answer 1 point Find m BCE F 3x 5 A D 7x 5 E 11x 3 B D C E

The following shape is a rectangle Find the missing sides Rectangle 1 P 10 S 24 T R 18 1 point 19 20 21 What is QR Type your answer 1 point What is SR Type your answer 1 point What is SQ Type your answer 1 point What is PR Type your answer

Using the coordinate plane determine which of the following are parallelograms 16 Parallelogram No Answers Chosen Possible answers W 7 4 X 1 6 Y 5 13 Z 1 12 J P 4 2 Q 6 4 R 11 2 S 2 3 E 0 8 F 6 10 G 2 0 H 4 2 K 7x 2 7 12x 22 M Not a parallelogram 1 point What is the value of x in the following parallelogram No Answers Chosen J 9 2 K 5 1 L 1 4 M 3 7 A 7 4 B 1 2 C 9 8 D 1 6 L

The quadrilateral below is a parallelogram Find the missing measures Parallelogram 2 F 21 C 71 E m FED 134 D 11 12 1 point m DEC Type your answer 1 point m CDE Type your answer 13 1 point m ECD Type your answer