2D Geometry Questions and Answers

Angles PTQ and STR are vertical angles and congruent P R Which chords are congruent O QP and SR O QR and PQ OPR and RS OPR and PS

In circle N KL ML Ex 4 J K 7x 7 N 13x 2 L M 8x 3 What is the measure of JNK O 66 O 74 O 77 080

In circle D ZEDH ZEDG E 57 9 4 3 F D 66 G C H What is the measure of EH O 114 123 228 O246

In circle T LPTQ RTS P T S O 4 3 66 R What is the length of PQ O 3 units 4 units 6 units O7 units

QR is tangent to circle P at point Q P 53 D R What is the measure of angle R O 37 O 53 O 90 O 97

In circle A ZBAE ZDAE 3x 24 B E X 10 A D What is the value of x O 14 O 17 O 27 O 34

Circle T has diameters RP and QS The measure of ZRTQ is 12 less than the measure of ZRTS S R P What is the measure of QP O 78 84 88 96

LK is tangent to circle J at point K L O 6 11 7 r K What is the length of the radius 6 85 O 85 12 O 121 36 O 157 12

In OH Kjk mik 11x 2 and mjk 12x 7 H K What is the measure of ikj mikj

Circle J is congruent to circle P K O M T P R If OK 2x QR 12 and RT x 3 what is the length of chord KM O 8 09 O 10 O 12

The UAV is flying at a speed of 13 meters per second in direction toward the fire Suppose the altitude of the UAV now 800 meters The new position is reprented at F in th figure A 0 6 O A D From its position at point F how many minutes to the nearest tenth of a minute will it take the UAV to be direc over the fire B 1 2 C 1 8 30 D 2 0 F

Circle A is congruent to circle J Chords BC CF EG KL LO and MP are congruent B C A G E D F L K M N O P Which arcs are congruent Check all that apply BCMP BC MO CF KP OEG KL OLOMP

AB is tangent to OC at point B and AD is tangent to OC at point D B 124 D A What is mZA O 34 O 62 O 56 O 124

X R 12 P 9 Q What value of x would make Ro tangent to circle P at point Q X

LN is tangent to circle O at point M and QM is a diameter P Q 42 O N 27 R M L Determine the measure of the following angles The measure of ZQML is degrees The measure of ZPMN is degrees

In circle Q ZRQS ZSQT U R T Which statement must be true ORT UT O ZRQT ZRST O RQL QT ORS ST

Chords DE EF and FG are congruent F E D 56 5 67 C 75 H G Determine the following measures mFG mZECF 0

The minor arc measures of circle Z are shown in the figure T 54 U 78 54 Y N V 71 71 X 32 W Use the drop down menus to complete each statement Angle UZT is congruent to angle Angle VZW is congruent to angle

Which figure shows a line tangent to the circle 6 9 3 5 10 5 LO 5 3

CB is tangent to OA at point C Find the radius A T T 5 C 8 B CB LAC by the radius tangent theorem so ZC is a right angle AABC is a right triangle so apply the Pythagorean theorem Use the steps and solve for the radius r 1 2 82 r 5 2 2 642 10r 25 39 10 54 25 64 35 89 10

LM is tangent to ON at point M L M 66 N Determine the following angle measures m M mZL O

B Check A E C D N V Y X W Given OA OV what congruency statements can you make Check all that apply OBCZY BEZX CB YZ OZDAB ZZVX DE WX BEZX

E B F In the figure ABCD is a lattice and AEFG is a square A AEFG 9 cm and Since IABI 4 cm is known C

Find the x and y coordinates of the terminal point for the angle estion 4 4 on the unit circle

8 C T 4 Points O Law of Sines O Law of Cosines b 15 75 25 a DETAILS LARPCALC11 6 2 032 NVA Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle a 10 b 16 C 650 B MY NOTES ASK YO Solve if possible the triangle If two solutions exist find both Round your answers to two decimal places If a triangle is r enter IMPOSSIBLE in each corresponding answer blank Y

Determine a general formula or formulas for the solutions to the following equation Then determine the specific solutions if any on the interval 0 2x sin 201 A 8 OB 0 O c 9 OD 0 OE There is no solution What is are the solution s to the equation sin 20 1 on the restricted interval 0 2x Select the correct choice below and if necessary fill in the answer box within your choice k or 8 k k0 kor 8 ecces kor 0 kor 8 kor 8 A 8 E Use a comma to separate answers as needed Simplify your answer Type an exact answer using a as needed Use integers or fractions for any numbers in the expression

Solids A and B are similar Use the given information and scale factor k from solid A to solid B to find the surface area of solid B Prism A has a surface area of 805 square feet and the and k The surface area of solid B is square feet 5

3 2 1 0 1 1 117 A 63 0 1 2 3 4 C 63 63 5 B 6 E 117 G 8 7 63 F 9 10 11 12 Figure 8 4 Explain why the parallelograms are congruent in terms of rigid transformations 5 Explain why the parallelograms are congruent in terms of corresponding angles and sides 6 Use notation like ABCD A B C D to state how the parallelograms are congruent Note that there c multiple correct ways to write this AMRG AKPS 7 Draw a picture that matches this situation

C B3 90 34 3 56 2 A 5 4 3 2 1 D E 11 10 1 0 1 56 2 90 343F 4 Figure 7 2 3 1 Explain why the triangles are congruent in terms of rigid transformations 2 Explain why the triangles are congruent in terms of corresponding angles and sides 3 Use notation like ACATADOG to state how the triangles are congruent Note that there are

h A cylindrical can has the following properties height h 21 6 cm and radius r 6 cm The company that makes this can wants you to minimize the materials needed surface area to create their can while maintaining the same volume Determine th

10 M 1 3 4 Find the formula for the graph of the function f x given in the graph above f x

Prok m 2 A landscape modeler uses a 3D printer to create plastic forms that will eventually be transformed into model trees The forms consist of a right square pyramid with base edges 6cm and a height of 10cm In the center of the base is attached a cylinder with a diameter 2cm and height of 3cm a Find the total surface area of the plastic form b Find the volume of the plastic form

1 point Find a possible formula for the trigonometric function graphed below Use x as the independent variable in your formula f x help formulas 5 18

Use the point slope formula to write an equation of the line that passes through form if possible The equation of the line is 0 0 0 8 X and has an undefined

1 point Assume that sin A sin B in the figure Find exact answers for each of the values below not decimal approximations All angles are given in radians and your answers should be in radians a If A then B b If A 1 1 then B help numbers help numbers sintet

Complete the table by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and Round your answer to two decimal places b a 45 a 55 0 b C C d d 80 0 O 4

Show that sin 0 O A O B O C 100 Which of the following four statements establishes the identity O D 1 82 cos 20 cos 40 sin 40 sin 0 sin 40 sin 0 1 cos 20 2 sin 0 sin 0 1 cos 20 3 2 8 1 cos 20 2 sin 0 sin 0 c 1 cos 20 2 2 11 3 8 1 2 3 8 2 cos 20 cos 40 cos 20 1 2 8 cos 40 1 cos 20 cos 40 8 3 1 1 82 cos 20 cos 40

Use a tree diagram for the following K a Find the number of ways 2 letters can be choosen from the set U V W if order is important and repetition is allowed b Reconsider part a if no repeats are allowed c Find the number of combinations of 3 elements taken 2 at a time Does this answer differ from part a or b GELLD a The number of ways to select 2 letters from the set U V W if order is important and repetition is allowed is

AXYZ T 1 R axis D AABC Draw A XYZ 02 9 the graph below if it is the case that T PENCIL THIN V 12 11 10 9 4 BLACK 6 5 20 2 A 12 114 10 9 8 7 6 5 4 2 B N M p S 99

6 Check if the triangles given below are similar Specify which triangles are similar Also write which method you used to decide similarity i e SSS SAS a E D LO b PQ SR 3 cm Angle P and S are 90 degrees B

7 Which shows the length of the darkened arc 7 5x 1 5x 15x G3T S zoom in 60 7 FORMULA n S 3 2 r 360 F H S

6What is the degree measure of RTU F 32 HD 238 G212 D 248 zoom in 32 S 6

In circle E with m DEF 78 and DE 20 find the area of sector DEF Round to the nearest hundredth F D E

Using the digits 0 to 9 at most one time each place a digit in each box such that the central angle is greater than 120 degrees C Central angle Inscribed angle Circumscribed angle 0 O D D Check

Team A and B love to play pickup basketball There are no fouls and no three pointers so all shots are worth 2 points The only problem is Team A always wins They typically play games to 100 and Team B loses by 10 points That is the typical final score is Team A 100 Team B 90 So they decide to increase the point value of each basket for Team B to 2 2 points Based on the typical results above what effect is this most likely to have The teams will tend to score the exact same number of points O Team A will still tend to win by 1 point instead of 10 Team B will now tend to win by a margin of 1 point Team B will now tend to win by 10 points

A simple dart target has two concentric circles The larger circle has a radius of 4 The smaller circle has a radius of 2 The scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring How many more points should a player receive for landing a dart in the inner circle as opposed to the outer ring The player should receive 4x times as many points The player should receive 2x times as many points The player should receive 9 times as many points The player should receive 3 times as many points

Let 1 3 2 and w 1 4 5 a Determine W 3 pts b c e d Determine 3 v 3 pts Determine 3 pts Find the unit vector in the direction of 3 pts Determine the dot product of and W 3 pts Angular coordinates Determing the angle between the vectors and w 3 pts

Convert the polar equation r 4r cose 3r sine to rectangular coordinates 8 pts

1 216 grams of salt has a volume of 100 cm3 What is the density of salt Given Formula Solution Answer 2 A ball has a mass of 46 9 grams and a volume of 40 5 cm3 What is the density of the ball Given Formula Solution

G D 83 66 F E What is the measure of minor arc EG 17 75 149 O211