2D Geometry Questions and Answers

Find 8 mi 1 and M22 56 2 9 10 117 2 2 108

7 Given quadrilateral TRAP with T 5 7 R 3 4 A 9 5 and P 1 10 Show TRAP is an isosceles trapezoid 3 4

6 Given AFUN with F 4 1 U 5 6 and N 1 3 Show AFUN is an isosceles right triangle righT ANgle 41 5 6 113

Find the standard form of the equation of the hyperbola with the given characteristics Foci 5 0 asymptotes y x

8 GARDENING A gardener uses a grow light to grow vegetable indoors If m 1 8x and m 2 7x 4 what is m 1 M21 8X 7 1846 11

13y 17 1 2 3 Given m27 38 and mz10 102 find the measure of each missing angle 4 3 5 6 29 x 3 15x 7 9 10 12 11 8 7 m 13 14 16 15

This is just a practice with some of the applications Please make sure you study all of the vocabulary for the unit too A large portion of the quiz is based off of the vocab Find the value of each variable 1 Note pl m P m 120 Co e d a b C d e

9 m2 DJP 10b 54 find the following D 3b 3 K 5b 27 P b mzDJK m DJP

A1 November 21 03 m2SUT 34 Find mz1 Find x if m2 4x 5 and A2 m151 A3 Find BD T A4 Solve for x 12 1 1 21 16 15 35

Geometry 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

The 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

Determine 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

Solve 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

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

1 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

Solve 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

Consider 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

Evaluate 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

Solve 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

Consider 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

Directions 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

Match 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

6x 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

B 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

4 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

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

Melissa 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

Question 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

Find 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

11 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

Sketch 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

3 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

Select 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

Draw 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

OP 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

Determine 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

Solve for Lc Submit your answer in terms of degrees A B 76

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

Joyce 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

Solve for Lc Submit your answer in terms of degrees B Show your work here 63

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

Which 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

Find the value of a to the nearest tenth X IC 8

Find the value of x Leave your answer in simplest radical form X 3

b g g h h 41 55 Y 33 8 B a a B Y d

4 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

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

Find 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

Write 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

1 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