Geometry Questions

6 Plot Figure ABCD given the points A 1 3 B 1 8 C 3 3 and D 1 2 10 S 10 10 Loid 4 points O on TBS HAW Ame d What is the most precise name for this figure 10 a How many sets of parallel sides does the figure have Show calculations to justify your answer 1 point b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer Irbe 2 points 2 points

2x 3y 4 and passes through the point 1 3 ay 3 x 1 by 3 x 1 y 3 x 1 d y 3 x 1 2 3 4 b c y x d y 5x 17 Which equation represents a line parallel to the y axis x 5 y 10 Which statement is true 2x Points A 5 3 and B 7 6 lie on AB Points C 7 6 and D 1 10 lie on CD a AB CD b AB 1 CD c AB CD are the same line d AB CD intersect but are not perpendicular c AB CD d Not enough information is given 3y 2x 4 33 Using the same information from the problem above which statement is true about the length of the segments a AB CD b AB CD 5 Below the equations of lines A B and C are given Determine whether each statement is true or false Line A y x 2 AIC WAS ALB Line B y 6 x 7 1 point each Line C 4x 5y 5

he given point on the unit circle find the six circular function values for s 8 X 17 the value of x or y as appropriate Then assumin X 0 Type an integer or a simplified fraction www

Graph the rational function Answer parts 1 through 7 below X 1 Select the symmetry of the function O The function is symmetric about the y axis O The function is symmetric about the origin O The function has no symmetry about the y axis or the origin 2 Find the y intercept Select the correct choice below and fill in any answer boxes within your choice OA The y intercept is Type an integer or a simplified fraction OB There is no y intercept 3 Find any x intercepts Select the correct choice below and fill in any answer boxes within your choice OA The x intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no x intercepts 4 What are the x coordinates of the vertical asymptote s Select the correct choice below and fill in any answer boxes within your choic OA x Use a comma to separate answers as needed COL OB There are no vertical asymptotes 5 What is the y coordinate of the horizontal asymptote Select the correct choice below and fill in any answer boxes within your choice OA y OB There is no horizontal asymptote 6 Type the y coordinate for each of the following points 2 2 4

3 Which ordered pair does not fall on the line formed by the other three Hint graph the points to the right 1 16 18 2 12 12 3 9 10 4 3 6 RDBTSNFO7654 Y 20 19 18 17 16 15 14 13 12 11 10 9 8 7 32 2 1 0 F 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X

estion 8 estion 9 estion 10 T corresponds to x Then findcos x andsin and state which functions are undefined for The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction 1 0 2 0 1 0 0 1

4 The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction 1 0 2 0 1

Lets 1 5 correspond to the point x y a Determine the quadrant where x y is located b Determine whether sins and cos s are positive or negative a Choose the correct answer below A Quadrant III B Quadrant II OC Quadrant IV D Quadrant I b is the value of the function cos 1 5 positive or negative Positive Negative Is the value of the function sin 1 5 positive or negative Negative O Positive

aces Dx where b 0 Determine the equation of the

50 Find the length of the pulley belt shown in Fig 2 87 if the belt crosses at right angles The radius of each pulley wheel is 5 50 cm C Fig 2 87

Let sec A 2 with A in QIII and sec B 5 with B in QII Answer exactly Find sec A B

and closer to the given angle than any other coterminal angle Give the quadrant of the angle if applicable A 103 Choose the correct graph below where the curve on each graph traces the angle beginning at the positive x axis and ending at the ray OA OB 100 B 48 103 F

coterminal with the given angle The correct expression is 315 Type an equation using n as

complementary angles with measures 3x 5 and 4x 31 The angles are Simplify your answer Type an integer or a fraction Type your answer in degrees Do not include the degree symbol in your answer Use a comma to separate answers as now

mea inal with A in degrees not equal to the given measure of the least positive angle that is The measure of the least positive coterms Simplify your answer

Type an equation using n

ind the angle of least positive measure in degrees not equal to the given with A 65 Simplif

radians Simplify your answer Typ

Find each measurement indicated 10 Find AB 27 m 16 C 13 Find Z C 80 A 17 7 mi 4 14 5 17 9 19 m Solve each triangle 14 5 in B 97 5 B B 28 7 mi 13 7 in A 25 6 mi C 11 Find AB 6 35 7 7 ZC 37 b 13 cm c 14 cm ZB 39 c 37 km a 23 km 8 A 17 13 in 14 Find 2 C B C 21 yd 93 14 in 9 in B 20 in C 33 27 yd 6 in A B 12 Find AC Answers Note answers may not be to the correct number of significant digits 1 7 yd 12 19 in 2 33 1 yd 13 39 8 3 28 9 m 14 137 15 22 16 LA 18 15 Find ZA 14 in B 16 mi 117 B 8 in C 117 27 in 28 mi 106 61 7 ZB 80 8 ZC 37 5 17 ZA 50 5 ZB 96 5 c 14 8 yd 18 ZA 22 1 ZB 51 9 c 33 in C C B 13 in

2x me complementary angle to IS 5 implify your answer Type a fraction with in the numerato

roblem 3 A rectangular plot of land is to be enclosed by a fence Furthermore an additional section of fence is set parallel to one side cutting the plot into two smaller rectangles If 288 meters of fence are available what is the greatest area of land that can be fenced in this manner

oblem 2 Suppose that a right triangle has legs of lengths 7 cm and 5 cm Note that the legs of a right triangle are the two sides that are not the hypotenuse A rectangle is inscribed in this right triangle so that two sides of the rectangle lie along the legs Find the largest possible area of such a rectangle

22 Given AB DF BC DE and AC EF B A Prove AABD D C AFDE F E

Q i ii A iii iv D 6cm 8cm B Q4 The diagram above shows the net of a right rectangular pyramid in which ABCD is base and 0 0 03 04 are brought together to form the vertex O When the solid is formed ABCD is the base AB 8cm AD 6cm and BO 13cm a Draw a sketch of the pyramid b Calculate the C height of the pyramid volume of the pyramid area of triangle AOB inclination of the triangle BOC to the hoge ABCD

34 Given BA CD ZADB LCBD Br N A Prove AABD ACDB 79 MX

36 Given KN bisects JM JK MN M K Prove AJKLAMNL N

32 Given R is the midpoint of PT 4P T and PRQ TRS Q M R PA Prove APQREATSR S AT 800

33 Given K N JK MN KL NO K K N J LM Prove AJKLAMNO DEL F 0

35 Given PQRS is a parallelogram P Q R Prove ARPS AQSP S OR T X IN

31 Given C is the midpoint of AE BA DE and ZA ZE B A C Prove AABC AEDC JE

24 Given ZJELM JK MN and K N K 0 Prove AJKL AMNO L N M

29 Given PS QR PQ SR P S He Prove APRSARPQ R

23 Given 4P ZS ZQ LT and QR TU AT RS Prove APQR ASTU P

19 Given ABDE BC EF and B E B A C D Prove AABC ADEF E F

20 Given PQ TU P T and Q U MER T P R S Prove APQREATUS U ZOMIA

niyal guibaoqeane 21 Given JK MN KL NO MICT K J Prove LO AJKLAMNO N M

26 Given PR TR P T P R Prove AABC ADBC S ORADE

27 Given LM JM L K 083 M Prove ALKMAJKM 10

07 11 01 MINEMEN 28 Given ABED A D B A C Prove AABC ADCE E OMAREXHIA

Use the figure to solve triangle ABC Round lengths of sides to the nearest tenth and angle measures to the nearest degree A Round to the nearest degree as needed Round to the nearest degree as needed B C O Round to the nearest degree as needed Find the measures of the unknown sides of triangle ABC O b a Round the final answer to the nearest tenth as needed Round all intermediate values to the nearest thousandth as needed 17 36 4 21 2 27 B a 13 7

A large warehouse has dimensions as shown The owner has it subdivided so that he can lease storage space to two businesses The area of the smaller space is 60x ft How could you express the area of the larger space in terms of x a 100 60 ft 100 x ft b 60 2 ft 60 100 C 3x d 60 100 x ft a 60 feet 100 feet

Select the correct equation of the following graph 10 10 10 10

cos alpha 8 17 and alpha is in quadrant III and sin beta 5 13 and beta is in quadrant I Find cos alpha beta

Intensity 2888 8 20 Peak 60 1 50 P 40 30 20 Procedures 1 2 10 40 45 50 hkl 110 200 55 4 Calculate lattice parameter a according to a d h k 1 5 Calculate the averaged lattice parameter a 2 60 65 Two Theta degree From the XRD pattern measure the 20 angle of the peak 1 2 and 3 Calculate and sin20 20 measured from the XRD pattern 3 Calculate lattice parameter d according to the Bragg s law 2dsin 0 2 where is wavelength 1 541 70 0 sin 75 d 80 3 a 85

Ccw counterclockwise 1 Translation 5 right and 5 up YA 2 3 2 1 1 3 Reflection Across the line y 1 YA i 3 2 1 5 Translation 5 left YA 5 2 1 11 2 3 4 12 3 3 4 5 4 5 formations 2 Reflection Across Line y x 4 3 5 2 1 A 3 3 2 4 2 1 1 4 Rotation 90 clockwise about the orig YA 5 2 3 4 1 4 3 2 1 1 2 3 5 V 2 3 3 2 1 1 1 4 6 Rotation 180 about the origin YA 5 3 2 1 1 6 2 1 4 1 5 3 4 2 5 3 4 5 Math Aids Com

H to MOH OH ASsys is expected to be negative a decrease in entropy because two molecules are converted into one molecule O AS sys is expected to be positive an increase in entropy because two molecules are converted into one molecule O AS sys is expected to be positive an increase in entropy because a cyclic compound is converted into an acyclic compound O ASsys is expected to be negative a decrease in entropy because a cyclic compound is converted into an acyclic compound

In the figure above O is the center of the circle and AD 10 If the area of the shaded region is 207 what is the value of a b c d

Write a rule to describe each transformation 19 X X W W Y

Given AD AB ABL BC and AD 1 DC Prove AABC AADC Step Statement AD AB AB LBC ADL DC try Type of Statement Reason Given B A D

Given AB LBC ADL DC and BC AD Prove AABC ACDA Step try Statement AB BC AD 1 DC BC AD Type of Statement Reason Given B