# 2D Geometry Questions and Answers

Geometry

2D GeometryGeometry 9 3x RE mz1 40 Classify by its angles 64 75 Exterior 30 10 2x mz1 38 For 12 14 find the measure of the exterior angle Hint you may need to find x first 12 13 14 Classify by its angles Exterior For 15 17 find the measure of each acute angle by finding x first 15 16 2x 2 45 3x 2 11 m21 17 60 Classify by its angles 60 3x 6 Exterior x 7 11x2 24 2x 18

Geometry

2D GeometryThe dimensions of a rectangular duct with grooved seam are height h 18 inches width w 28 inches length 3 5 ft M 3 8 inch A Find in inches the value of the Length of the Stretchout L S 13 75 B Find in inches the value of the Width of the Strechout W S 70 75 MY F Xinches State your answer as a decimal value Do not ro Xinches

Geometry

2D GeometryDetermine the remaining sides and angles of the triangle ABC A 19 39 B 20 57 c 16 98 m C Question 8 7 1 23 Part 1 of 3

Geometry

2D GeometrySolve the triangle What is the length of side a A 0 C 13 26 C 20 a Round to the nearest whole number as needed What is the measure of angle B B Round to the nearest degree as needed What is the measure of angle C 0 Round to the nearest degree as needed a B

Geometry

2D GeometryK Solve the triangle shown to the right A B and C Round to the nearest tenth as needed 15 A 15 17 B

Geometry

2D Geometry1 Find the area of the triangle using the formula A bh and then verify that Heron s formula gives the same result Use the formula A he area is 1 zbh

Geometry

2D GeometrySolve each triangle ABC that exists A 38 a 3 4 c 14 3 Select the correct choice below and if necessary fill in the answer boxes within the choice OA There are two possible solutions for the triangle The measurements for the solution with the longer side b are as follows B C b The measurements for the solution with the shorter side b are as follows B C b Round to the nearest tenth as needed B There is only one possible solution for the triangle The measurements for the remaining angles B and C and side b are as follows B b C Round to the nearest tenth as needed C There are no possible solutions for the triangle

Geometry

2D GeometryConsider circle E CD is the perpendicular bisector of segment AB B C What is the measure of the arc intercepted by ZACD A D 50 180 270 E 90 D B

Geometry

2D GeometryEvaluate the given trigonometric function directly without first changing the radian measure to degree measur sec 4 3186 sec 4 3186 Round to four decimal places as needed

Geometry

2D GeometrySolve the equation for all exact solutions where appropriate Round approximate answers in degrees to the nearest tenth Write answers using the least possible nonnegative angle measures sin 0 cos 0 sin 0 0 Choose the correct answer below OA 270 n where n is any integer O B 0 OC 180 n where n is any integer O D 90 n where n is any integer

Geometry

2D GeometryConsider the following 25x 4 300x 40y 900 0 a Find the standard form of the equation of the ellipse b Find the center vertices foci and eccentricity of the ellipse Order your answers from smallest to largest x then from smallest to largest y If the ellipse is degenerate find its center then enter NONE in Centers Vertices Foci Eccentricity c Select the correct graph of the ellipse Use a graphing utility to verify your answer 10

Geometry

2D GeometryDirections Show and explain mathematical work for ALL problems Part I Multiple Choice Each question is worth 2 points 1 As shown in the diagram below when hexagon ABCDEF is reflected over line 7 A B C D E F A E B D C C m Im B A E F F Under this transformation which property is not preserved a area b distance c orientation d angle measure

Geometry

2D GeometryMatch the equation with its graph 16 O O 10 10 5 y 10 5 5 10 y 10 10 5 10 5 10 5 5 5 5 y 5

Geometry

2D Geometry6x 7 J M If JL 16 and KM is a perpendicular bisector of JL determine which of the following claims are True A JM 8 B JK LK 5x 3 L D LK 17 True True C JK 11 True True False False False False

Geometry

2D GeometryB O D mi 1 2 E 4 3 If m 22 78 which of the following angles also measure 78 Select THREE that apply A 23 5 6 8 7 24 25 26 a 27 b

Geometry

2D Geometry4 Question 4 10 8 6 4 2 Question 4 If ATUV is translated to image ATUV as shown below by the rule z y z 8 y 3 what are the coordinates of ATUV 10 8 96 4 2 2 4 6 9 8 10 Y II Pause Q Zoom T U 2 4 6 8 10 X V

Geometry

2D GeometryWrite the equation of the circle in standard form Then identify its center and radius 9x2 9y2 72x 54y 104 0 Center Radius

Geometry

2D GeometryMelissa needs to translate a figure six units to the right and two units down Which of the following rules correctly represents that translation A z y z 2 y 6 z y z 2 y 6 z y 2 6 y 2 x y z 6 y 2 B C D

Geometry

2D GeometryQuestion 3 of 7 3 Assume each outcome in the sample space represented by the Venn diagram below is equally likely Find P AIB A Answer B

Geometry

2D GeometryFind the center radius form of the equation of the circle described and graph it center 0 2 radius 2 Type the center radius form of the equation of the circle x y 2 Type an equation Simplify your answer Graph the circle 4 Click to enlarge graph 10 Ay 10

Geometry

2D Geometry11 AB is a vector whose tail is at 4 2 and whose head is at 1 3 a Calculate the magnitude of AB b Determine the coordinates of point D on vector CD if C 6 0 and CD AB c Determine the coordinates of point E on vector EF if F 3 2 and EF AB d Determine the coordinates of point G on vector GH if G 3 1 and GH AB

Geometry

2D GeometrySketch a picture with the coordinates of the unit circle on the terminal side clearly labeled assuming the given angle is in standard position Use the picture to find the exact value a sin 4 3 b tan 5 se 3 4

Geometry

2D Geometry3 7 6 5 44 3 2 1 7 6 5 4 3 98 2 1 2 3 6 7 8 9 y 1 2 3 4 5 6 7 X 8 Position the four points so they do not coincide and so they all lie on the graph of the same logarithmic function

Geometry

2D GeometrySelect the true statements to determine whether ADAC is congruent to ABCA B Show your work here ZACBZCAD 46 The triangles are not congruent AB AD C The triangles are congruent by the SAS criterion 46 ZCABZDCA A The triangles are congruent by the AAS criterion The triangles are congruent by the ASA criterion D

Geometry

2D GeometryDraw the image of the triangle under a dilation about the origin with a scale factor of 2 Show your work here 14 12 10 8 6 4 144 12 10 8 6 6 6 8 10 12 13

Geometry

2D GeometryOP and MN are parallel Select the valid statements used to prove whether APMO is congruent to ANOM Select as many as apply M Show your work here MOOM MN MO P ZNZP 25 ZOMN ZMOP because they are alternate interior angles The triangles are congruent by the AAS criterion The triangles not congruent 25 N O

Geometry

2D GeometryDetermine whether the triangles are congruent Note the triangles are not drawn to scale 8 Congruent 22 28 63 Show your work here 28 8 O Not congruent

Geometry

2D GeometrySolve for Za Submit your answer in terms of degrees Show your work here 113 a A B

Geometry

2D GeometryJoyce is building a railroad track that crosses the road at an angle The rails of the track must be parallel The sides of the road are parallel What must be the measure of z 1 124 I

Geometry

2D GeometryAre the lines Y and Z parallel The figure may not be drawn to scale Y Z Show your work here 43 137

Geometry

2D GeometryWhich name refers to the same line as DB O EA C O P m A Show your work here E B n F P O OF m G D

Geometry

2D Geometry4 Use the given information to determine the remaining five trigonometric values a Sin A 4 4 7 b 7 b tan A 2 1 2 1 2 1 2 1 H A

Geometry

2D Geometry4 Suppose is an acute angle and cos B find sin and tan Two ways to do this b 4 B 7 OR

Geometry

2D GeometryFind the values of the six trigonometric functions of 0 adj 8 sin cos tan 0 0 17 hyp a 15 opp csc sec cot 0 a 8 17 a 64 289 a 225 a 15

Geometry

2D GeometryWrite the expression in terms of sine and cosine and simplify so that no quotients appear in the final expression 1 cot 8 1 cot 0 ese20

Geometry

2D Geometry1 C 27 G C A 38 36 8 B F B 42 d d2 C 63 d d m ABC m CBE m CFE m EFG m BCF 27 m BEF 36 m BDF D 72 E 81

Geometry

2D Geometry1 40 Find the equation for the parabola that has its vertex at the origin and has directrix at x The equation is

Geometry

2D GeometryOASA right SAS SSA Question 24 How many triangles are possible with the configuration A 60 5 a 34 2 b 38 0

Geometry

2D GeometryTry This Match the function to the correct list of transformations One is done for you Function B f x x 1 3 f x 3 x 2 1 f x 3 x 1 2 3 x 1 x 1 List of Transformations A Horizontal compression shift right shift up B Vertical reflection vertical compression shift down C Horizontal stretch shift down D Vertical reflection vertical stretch shift left shift up

Geometry

2D Geometry10 45 10 8Y 6 4 2 2 4 6 8 10 M 2 es t 7 x 10 Q Write the standard equation for the hyperbola graphed above

Geometry

2D GeometryGraph the given hyperbola 4x 25y 16x 200y 484 0 Graph by selecting the correct hyperbola clicking the center then clicking the point on the graph 10 9 8 7 6 5 4 3 10 9 8 for 7 6 No 4 4 2 3 5676 5 8 9 10

Geometry

2D Geometrytch the graphs to their equations y 3 x 2 1 4 x 2 1 y 3 1 y 3 4 x 2 4 1 1 1 a b 7 7 654 3 2 1234 2 4 6 7 of 3 7 6 5 4 3 2 1 5 6 7 74 6 3 2 123 56 67

Geometry

2D GeometrySketch a graph of x 4 y 1 71 65 6 4 32 3 7 7 6 5 4 3 2 1 1 2 3 4 5 6 1 71 1 2 3 4 5 6 7

Geometry

2D GeometryA swimming pool has the shape of a box with a base that measures 26 m by 19 m and a uniform depth of 2 9 m How much work is required to pump the water out of the pool when it 3 is full Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity Draw a y axis in the vertical direction parallel to gravity and choose one corner of the bottom of the pool as the origin For 0 sy 2 9 find the cross sectional area A y A y 494 Simplify your answer Set up the integral that gives the work required to pump the water out of the pool Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA JO dy OB CHEER dx