Geometry Questions

17 At what angle A shown below should the support for 0 5000 5 75 4 2 9375 6 5 A 3 0625

In the figure below a 9 b 11 and d 13 Use this information to solve the parallelogram for x The diagonals of the parallelogram are represented by c and d Round your answer to two decimal places X b a 8 ficuno no drawn to gaala

11 Use the Law of Sines to solve if possible the triangle If two solutions exist find both Round your answers to two decimal places A 60 a 13 b 11 6 B 50 6 C 69 40 c 14 05 B 29 C 91 c 13 B 69 40 C 50 6 c 11 6 B 91 C 29 c 14 05

5 Given C 116 a 13 9 and c 9 3 use the Law of Sines to solve the triangle if possible for the value of b If two solutions exist find both Rou your answer to two decimal places b 1 99 and 6 31 b 1 06 and 6 44 b 4 43 not possible b 7 68

Use the law of Cosines to solve the given triangle Round your answer to two decimal places a 9 b 4 5 C 110 b C a B

ladder of length 10 ft has a distance of 6 ft from a wall To what height does the ladder reach wall 10 ft ladder 6 ft O 1 8 ft O 2 60 ft O 3 16 ft 4 4 ft

Consider the following sin 10 cos 0 a Eliminate the parameter to find a Cartesian equation that represents the curve 2 F Cloudy X sin CHOICE A b Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases CHOICE B 0 CHOICE C y 0 0 5 0 5 y 0 2 0 4 0 6 0 8 1 0 y 0 2 0 4 0 6 0 8 TE SOST 1 0 0 5 0 5 Q Search X 1 0 CHOICE D 1 0 0 5 0 5 y 1 0 0 8 0 6 0 4 0 2 0 8 0 6 0 4 0 2 0 5 0 5 1 0 1 0 A

Find the total area of the shaded regions 6 RE 16 x 16x U COB The total area of the shaded regions is Type an integer or a simplified fraction

equation below gives parametric equations and parameter intervals for the motion of a particle in the xy plane Identify the particle s path by finding a Cartesian equation for it Gra Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 5t 6 y 25t o t Find a Cartesian equation for the particle s path 10 y Graph the Cartesian equation below Indicate the direction of motion as t increases Choose the correct graph below OA O C OB 10 10 A TO Q 14 A point s possible This question 4 point s possible Q Indicate the portion of the graph traced by the particle Select the correct choice below and if necessary fill in the answer box to complete your choice A The portion of the graph where t is greater than B The entire graph C The portion of the graph where t is less than OD Sul

10 Consider the function y 3 x 2 8 a State the transformations the b Graph the parent function c Graph the transformed function 1K Show your work in the table below or graph all the transformations on the grid provided In 8

Theorem 3 12 Lines Perpendicular to a Transversal Theorem In a plane if two lines are perpendicular to the same line then they are parallel to each other If m 1 p and n 1 p then m n Notes Extra Practice In Exercises 1 4 find the distance from point A to BC Ay 1 3 3 0 A B 4 B 1 3 2 3 4 A 3 3 4 2 Ay 4 C D 0 1 3 2 D 1 2 4 x 2 C 1 1 4 x Use the distance formula for 1 4 2 4 A 3 4 4 2 4 2 Ay 4 2 2 C 1 4 D 0 4 D 3 2 B 4 A 1 3 C Am n FF 4 1 X 3 2 B 1 2 4 x

In Exercises 5 8 determine which lines if any must be parallel Explain your reasoning 5 6 7 8 p HI p Am Am n n 1 2 S a k t

12 in 45 a 30 b zoom in 4 4 X given this triangle Find a and b given this triangle You can format your answer like a 38 in b 5 13 radical 17 if you cannot find how to enter radicals on your chromebook Include units in at the end of each answer a 5 b 7

7x 15 12 in x 28 4x 3 zoom in 3 Find x given this triangle Find a and b given this triangle You c wer like a 38 in b 5

3 Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle Then solve the triangle a 8 c 5 B 40 Law of Sines A 102 34 C 37 66 b 5 26 O Law of Sines No solution Law of Cosines A 37 66 C 102 34 b 5 26 Law of Sines A 37 66 C 102 34 b 5 26 Law of Cosines A 102 34 C 37 66 b 5 26

24 Given that KM is the perpendicular bisector JL prove that JK LK 24 Given that KM is the perpendicular bisector of JL prove that JK LK Use the word phrase bank to complete the paragraph proof 1 KM is the perpendicular bisector of JL KML and 2 are both of perpendicular lines KM KM by the Triangle QTR Triangle SRT by the Therefore JK LK because congruent A Reflexive Property B Corresponding C Alternate Interior D Angle Angle Side Congruence E Angle Side Angle Congruence F Side Angle Side Congruence 5 6 4 3 by definition of a bisector G Right H Congruent J KMJ K MLK L JK LK M JM LM Theorem Langles by definition parts of congruent triangles are

16 A line segment has endpoints 2 7 and 5 4 The line segment is dilated by a factor of 3 around 4 3 What are the new endpoints and length of the line segment 17 P State whether the two triangles are similar and explain why T 100 45 100 R s 35 U 18 Given line m and point 0 not on line m The image of line m is constructed through a dilation centered at 0 with a scale factor of 3 Which of the following statements best describes the image of line m a line passing though point 0 c a line parallel to line m b a line intersecting with line m d a line perpendicular to line m

21 In Triangle PQR if PR is extended through R to T If QPR 3x 6 and PQR 2x 6 and QRT 150 degrees Find the value of x

19 Find the coordinates of the center of dilation What would be the scale factor if it is an enlargement What would be the scale factor if it is a reduction

21 In Triangle PQR if PR is extended through R to T If QPR 3x 6 and PQR 2x 6 and QRT 150 degrees Find the value of x

Q13 Which of the following operations is NOT closed under polynomials a Addition b Subtraction c Multiplication d Division

25 Spiral based on Question 5 2b test Triangle ABC DEF if A x 45 and C 35 and D 60 Then Find A Hint what is true about the angles in congruent triangles

26 Spiral based on Question 10 2b test 6x 7 2x 103 x

20 Which triangles are similar to triangle ABC where Angle A is 70 degree and angle C is 10 degrees A Triangle DEF where D is 70 degrees and F is 10 degree B Triangle GHI where G is 70 degree and H is 10 degree C Triangle JKL where K is 100 degree and L is 10 degree D Triangle MNO where M is 70 degree and N is 100 degree

X 22 5 x A C B 150 erf anwa asi o rio

e cos sin 3 f cos tan

8 Graph each function a y sin x b y cos x c y tan x

sin sin 4 d

9 Evaluate each of the following a sin 2 b arccos 2

5 sin x cos x 1 0 x

8 Triangle A B C is the image of ABC after a dilation of 2 Which statement is true a AB A B b BC 2 B C c mzB mzB d mA 1 2 m A

of congruence to decide if the two figures are congruent Explain your answer Give Coordinate Notation for the transformation you use Question 11 Question 12 N D B E 4 V 4 C 8 8 C D 0 4 8 8

6 What will be the coordinates of point R if figure PQR is reflected across the y axis 6 3 2 1 5 3 2 3

9 Line segment AB is shown in the diagram below Which two sets of construction marks lobeled I II III and IV are part of the construction of the perpendicular bisector of line segment AB X IV oll and II b I and III c II and t d Il and iv X 2 ac i 90 degl

5 What will be the coordinates of point R if triangle RQS is rotated 90 counterclockwise 10 B 6 4 2 10 8 6 4 2 2 4 6 8 10 R 2 a 5 N 6 8

3 On the set of axes below pentagon ABCDE is congruent to A B C D E Which describes a sequence of rigid motions that maps ABCDE onto A B C D E 1 a rotation of 90 counterclockwise about the origin followed by a reflection over the x axis 2 a rotation of 90 counterclockwise about the origin followed by a translation down 7 units 3 a reflection over the y axis followed by a reflection over the x axis 4 a reflection over the x axis followed by a rotation of 90 counterclockwise about the he de origin of congruence togler 16

7 Triangle A B C is the image of ABC after a dilation centered at the origin The coordinates of the vertices of ABC are A 2 1 B 2 4 and C 2 3 C If the coordinates of A are 4 2 the coordinates of B are a 8 4 b 4 8 c 4 6 d 1 2

10 Which diagram shows the construction of the perpendicular bisector of AB 71 5 1 A B 3 4

4 a What is a single transformation to describe the figures in the graph b What is a sequence of transformation to describe the figures in the graph 10F D 8 AA 6 4 A B 8 6 4 2 2 B 2 4 6 8 10

1 Triangle TUV is shown on this coordinate plane G 3432 79 A 0 4 2 3 4 1 2 3 4 5 6 B 4 0 X Triangle TUV will be reflected over the x axis The image of TUV will then be translated 2 units up and 1 unit left What will be the coordinates of the final image of point V after the two transformations C 4 6 D 6 4

2 What will be the new coordinates of the figure if it is translated using the function rule x y x 2 y 6 A P A L P V

Based on past experience a plumber believes that 8 of the people who hire a plumber will not payment their bill on time The plumber has recently completed 200 jobs What are the mean and standard deviation of this model mean standard deviation accurate to 3 decimal places What is the probability that over 10 of these clients will not pay the plumber on time

The Lewis Broadcasting Tower in Columbus Georgia is approximately 1 tall If you are on level ground exactly 5280 feet one mile from ba tower what is your angle of elevation looking up at the top of the towe answer in degrees Oal 14 0 Ob 14 4 Od 76 0 d 43 5

3 Sketch 4 2 cos 5 x 60

Given COS 2 sin x y 204 325 36 325 36 325 O 204 325 24 25 in Qll and Sin y 130 QIV FE

6 Classify the angle pairs as corresponding alternate interior alternate exterior or consecutive interior angles 1 3 24 5 7 6 8 a Angle 3 and angle 5 b Angle 1 and angle 8 c Angle 6 and angle 3 d Angle 4 and angle 8

9 Given DE HG DE II GH Prove DF HF D E H Statement Reason

In 12 13 Find the indicated information drawings are not to scale 12 13 1429 9x 5 12r 26 8x 2 Find the length of each side

In 1 Identify the following angle pairs as Corresponding Angles Alternate Interior Angles Same Side Interior Angles Vertical Angles or Linear Pairs a 23 and 25 b 28 and 25 c 24 and 28 d 22 and 28 c 24 and 23 2 5 7 86

8 Given HI JK AHMK is isosceles Prove AHMI AKMJ M K Statement Reason