2D Geometry Questions and Answers

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

Parallelogram 4 Opposite angles are Answer perpendicular supplementary congruent complementary 1 point Consecutive same side angles are Answer bisect bisect congruent complementary DA

Parallelogram 2 Opposite side are parallel supplementary perpendicular complementary 1 point bisect bisect Answer Opposite side are Answer congruent perpendicular

X 17x 3 S 8 Given AMTW ABG T G 4x 3

stance is 8 3 Z 6 3t Type an exact answer using radicals as needed Try again The distance from a point S to a line that passes through a point P and is parallel to a vector v is given by the formula below where PS is the vector that has initial point P and terminal point S Distance PSXV v

Arrange the following step Prove cosa sin a tan a A cosa sin B COS sin a cos a

Find the distance from the point to the line 2 1 1 x 1 t y 1 2t z 6 3t The distance is Type an exact answer using radicals as neede

Find the equation for the plane through the points Po 1 2 3 Qo 2 1 2 and Ro 4 3 1

23 What is sin 550 equivalent to A sin 80 B sin 10 C sin 10 OD sin 80

19 Which of the following is the correct graph of the angle 128 in standard position A B C D 128 128 t 128 128

17 Which of the following is the correct graph of the angle 305 in standard position A OB O C D 305 305 305 305

25 What is sec 246 equivalent to O A OB sec 24 C sec 66 sec 66 OD sec 24

24 sin 550 OA 9848 OB 9848 OC 1736 OO D 1736

21 What is tan 212 equivalent to OA tan 32 B tan 58 C tan 32 D tan 58

20 What is the measure of the reference angle of 128 OA 52 B 232 O C 38 D 128

14 Find the following function value to four significant figures cot 8 13 A 6 885 OB 6 925 O C 6 910 D 6 869

18 What is the measure of the reference angle of 305 A 55 B 35 C 65 D 25

Which of the following transformations appears to be a trans O

5 In right triangle ABC AC 17 AB 7 Determir the length of BC in simplest radical form a 4 15 b 60 2 30

4 In the diagram below MR 8 Determine the length of NM and RN R 60

2 In right triangle ABC below AC 9 What is the length of AB a 4 5 b 3 3 c 6 3 d 18 A 60 B

1 Simplify the following expressions a 10 x 3 b 2 2 x 3 C 3

7 A B C In the figure above what is the value of x 2 6 6 6 2 2 3 45 X

write a sytem of linear equations that fits the desrciption the solution of the sytem is a point on the line y 9x 1

In the xy plane the point 2 6 lies on the graph of the function g x 2x kx 18 What is the value of k

A rectangular container with a base that measures 10 feet by 10 feet is filled with jelly beans The container is divided into regions each with the same height as the container and a square base with sides that measure 1 foot each Sherman randomly selects ten of these regions and counts the number of blue jelly beans in each region The results are shown in the table below Region Blue Jelly Beans I 20 II 21 III 27 IV 31 V 19 Region VI VII VIII IX X A 25 000 B 2 500 C 250 D 25 Blue Jelly Beans 22 25 24 28 23 Which of the following is a reasonable approximation of the number of blue jelly beans in the entire container

26 F X O bea G In the circle above the length of arc FXG is 14 If FG is a chord that passes through the circle s center O what is the length of the segment XO A 7 B 14 C 28 D 56

20 Mass kg 60 000 55 000 50 000 45 000 40 000 Volume versus Mass 10 10 5 11 11 5 12 11 11 5 12 Volume m 12 5 13 13 5 14 Selin weighs 14 different objects of similar density The scatterplot shown above shows the volume of ea object and the corresponding weight of each object The line of best fit for the data is shown above For object that had a volume of 11 5 m the actual mas was about how many kilograms more than the ma predicted by the line of best fit A 1 000 B 2 000 C 3 000 D 4 000