Geometry Questions

Using the figure provided complete each congruence statement Explain your reasoning B A 2 E ZBED H D C

15 One litre of latex paint covers approximately 8 5 m and costs 12 a Copy and complete this table Volume of Paint p L Cost c 0 24 Area Covered A m 0 17 0 2468 b Graph the area covered as a function of the volume of paint c Graph the area covered as a function of the cost d Write the domain and range of the functions in parts b and c

each congruence statement Explain your reasoning A E DBC B D LCDB

3 On Sunday Tiana runs on a straight path to the park located at 8 12 on the grid and from there she runs on a straight path to her friend s house located at 10 6 on the grid From there she runs on a straight path back to her house Ronald runs on a straight path to the library located at 12 0 From there he runs on a straight path to the store located at 10 6 From the store he runs on a straight path directly back home Draw the routes on the coordinate plane 4 Demonstrate that the two triangles formed by their routes are congruent Include a triangle congruence statement Then determine a series of transformations that maps one triangle onto the other

2 Tiana and Ronald like to run as part of their exercise routines on the weekend They each go on runs from their house Tiana s house is located at point T and Ronald s house is located at point R on the coordinate plane shown LI V 20 12 R 10 12 14 1 On Saturday Tiana runs 3 miles north then 4 miles east and then back to her house via the shortest route Ronald runs 3 miles west then 4 miles south and then back to his house via the shortest route Draw the routes on the coordinate plane Demonstrate that the two triangles formed by their routes are congruent Include a triangle congruence statement Then determine a series of transformations that maps one triangle onto the other

a sin 0 b cos 8 c tan 0 d cos 20 e tan 20 cot 20 g sec 20 h CSC 28 12

Use a double angle formula to rewrite the expression Use a graphing utility to graph both expressions to verify that both forms are the same 8 sin x 4

Solve for the variables and find missing values Classify the triangle by the sides and angles 5 DE E 5x12 3x 4 F 6 3x 2 z 5 y 3 2x 5

Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle a 11 b 13 c 8 Law of Sines O Law of Cosines Then solve the triangle Round your answers to two decimal places A B C Mond 11 n O

Find the slope of the curve below at the given points Sketch the curve along with its tangent lines at these points R r 9 9 cos 0 0 2 T The slope at the point 0 2 Simplify your answer is www

Sketch the region defined by the inequalities 3 r 5 and Choose the correct graph below O A O B ses IN 2 O C X G D tio

an 2 given tan 7 3 with 180 B 270

148 A 2x 15 8 C

HQ Four Quadrant Ordered Pairs B C 3 3 G E C Z 4 3 2 4 S Write the ordered pair for each given point 8 4 9 W 11 I 10 12 Z 2 2 2 1 1 2 4 4 5 8 Tell what point is located at each ordered pair 1 3 7 3 6 4 2 8 7 4 9 7 8 9 5 8 9 6 3 8 13 G 14 T Plot the following points on the coordinate grid 17 O 7 4 19 V 2 5 18 F 3 6 20 A 2 9 W X messa 21 Y 1 6 22 U 2 5 1 2 6 1 D 7 4 4 8 1 3 15 D 8 6 16 J 3 1 23 M 1 5 24 N 8 8

Chapter b The report also gave data on the percentage of children who were not covered by health insurance for four groups Hispanic children with both parents foreign born Hispanic children with at 1Q least one U S born parent Non Hispanic White children and Non Hispanic Black children Those data were used to create the time series plots for these four groups shown below The data for all children are also included in the plot Uninsured 25 20 15 10 5 0 2010 2012 2014 Year Non Hispanic White children Non Hispanic Black children Hispanic children with foreign born parents Hispanic children with at least one U S born parent All Children Hispanic Foreign Born Parents Hispanic At Least One U S Born Parent Based on this the title of the report Select and the group showing the lowest rates is Select Non Hispanic White Non Hispanic Black 2016 2018 Write a paragraph based on this plot that comments on the similarities and differences of these groups Also explain whether the title of the report is or is not supported by these time series plots Bb Over time the percent of Hispanic children with foreign born parents who are uninsured appears to be Select who are uninsured appears to be Select 8 the percent of Hispanic children with at least one U S born parent e the percent of Non Hispanic White children who are uninsured appears to be Select B and the percent of Non Hispanic Black children who are uninsured appears to be Select B However if we look only at the last three years the percent of uninsured children in the following groups appear to be increasing Select all that apply G to be supported Additionally the group showing the highest rates of uninsured children is Select B

7 6 A 10 9 8 7 6 5 4 3 fy 2 3 4 5 6 7 8 9 10 B 2 3 4 5 6 30 8 Position points A and B so they both lie on the graph of f g x

F C Q A 10 y 8 6 4 4 2 0 2 2 6 8 10 2 B E 4 D X 6 Move the points so that they all lie on the graph of f x x 4 x 3 x 5 x 1 x 2 and do not coincide

6 4 C 10 A 8 6 4 1 2 0 2 4 6 8 10 y 2 B 4 D 946 X Move the points so that they all lie on the graph of f x x 4 x 3 x 5 60 and do not coincide

A 10 y 9 8 7 6 5 4 3 fr 3 J5 5 6 7 8 9 10 23 5 6 8 Position points A and B so they both lie on the graph of f g x

3 3 6 7 9 8 7 65 9 4 3 2 1 2 3 4 5 6 7 8 Y 1 2 3 4 4 2 5 3 6 Move the points so they do not coincide and both lie on the graph of fog f x x 1 g x x 2

8 The graph of a function h is shown Graph the inverse of h on the blank coordinate grid 10 5 0 5 0

quadratic function f x 4x 48x 128 Give the a vertex b axis and d range ex is dered pair

K For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is 00 00 Type your answer in interval notation The range is 0 2 Type your answer in interval notation b Give the coordinates of the vertex The vertex is 0 Type an ordered pair 986 10 2 4 6 x 4

Sore 23 Penalty back to zero Question Watch Video In the diagram below of triangle RST U is the midpoint of RT and V is the midpoint of ST If m TRS 33 5r and m LTUV 39 Se what is the measure of TUV Show Examples w UMAN S ay as and F PANG Toan ayam amare d Viruses found And

Draw AMGT Use the triangle to answer the questions below 1 What angle is included between GM MT and ZT 2 Which sides include 3 What angle is included between GT MG and

Given ARST with a point U inside such that ZRST ZRTS 42 and ZRSU ZSRU 18 Find ZUTS S U R

26 Given APOR ASTU m P 5x 30j mLQ 7x 35 mLT 4x 12y mzU 8y 2 Find MLP MLQ m R y MLS MLT mLU SHOW WORK You might want to draw a picture to help you get started but you don t have to

25 mm 60 60 These figures are congruent What is men 50 mm 30

Find the point on the curve h x x2 8 that is closest to the point 18 8 Enter your answer as an order pair

Using the prototype oblique triangle shown below and the information given find the measure of the remaining sides and angles in the triangle b a 7 C a If b 9 68542 y 124 and a 3 50173 then B

A right circular cone has a radius of 2x 4 and a height 5 units less than its radius Express the volume of the cone as a polynomial function The volume of a cone is Vr h for radius r and height h Enter as pi help formulas V x

A rectangle has a length of 12 units and a width of 6 units Squares of x by x units are cut out of each corner and then the sides are folded up to create an open box Express the volume of the box as a polynomial function in terms of x f x help formulas

Population standard deviation 23 N 49 X 14 a Set up a 98 C I E for population Mean b Set up a 95 C I E for population Proportion c Between what two values around the mean 99 of observations fall d Between what two values around the mean 98 of observations fall e Above what value only 2 of observations fall f If s 23 do parts a and b

The angle bisectors of AXYZ are XG YG and ZG They meet at a single point G In other words G is the incenter of AXYZ Suppose FG 17 YG 18 mz DXF 92 and m2 EYG 24 Find the following measures Note that the figure is not drawn to scale X D Y F E m LEYD DG 0 0 m LEZG 0 00 X UIU

4 Find all points on the curve r 2 2 cos 0 where the tangent line is vertical List the points in polar form

1 8 Write a polar equation of a conic with the focus at the origin and the given data 1 Ellipse eccentricity 12 directrix x 4 2 Parabola directrix x 3 3 Hyperbola eccentricity 1 5 directrix y 2

Point Q is the midpoint of PR and PR 21 75 yards What is the length in yards of QR

The following graph shows a proportional relationship What is the constant of proportionality between y and in the graph 54 6 5 8 ON 1 29 3 4 12 5 Constant of proportionality 6 x

Find the exact value of each expression it it is defined If an answer is undefined enter UNDEFINED a tan 0 b tan sqrt 3 c tan sqrt 3 3

29 C 1 sino A r 3 sing intersection ts 12 n

Part B Draw DE parallel to BC You can draw DE any length and place it anywhere on the coordinate plane but not on top of AABC Find and record the ratio n of the length of DE to the length of BC Then multiply the lengths of AB and CA by n and record the resulting lengths

In Exercises 7 and 8 sketch a diagram of the description 7 RS bisecting KL at point R In Exercises 9 14 use the diagram to determine whether you can assume the statement 9 Planes A and B intersect at EF 10 Points C and D are collinear 11 HJ and ID are perpendicular 12 GD is a bisector of EF at point D 8 AB in plane U intersecting CD at point E and point C not on plane U 13 IHHG 14 ZHJD and ZHDJ are complementary angles C IG D B

6 A reservoir R supplies two towns Alton and Barnsville with water The pipelines from R to each town are being replaced to cope with increased demand The towns are connected by a straight road through them and the reservoir is 7 km from this road 4 km R 7 km 11 km B a Find the distances AR and BR to the nearest metre b Find the total cost of the new pipelines given that each 100 m will cost 2550

1 The shadecloth outside a workplace is 3 m long The building is 2 4 m high How far are the pegs from the base of the building 2 A city park is a square with sides 320 metres long The council decides to build a new walkway from one corner to the opposite corner How long will the walkway be B 3 2 m 14 2 m shadecloth 3 m 2 4 m building Find the length of the truss AB for the roof structure shown

In Exercises 3 6 use the diagram to write an example of the postulate 3 Two Point Postulate Postulate 2 1 4 Line Point Postulate Postulate 2 2 5 Plane Point Postulate Postulate 2 5 6 Plane Intersection Postulate Postulate 2 7 In Exercises 7 and 8 sketch a diagram of the description 7 RS bisecting KL at point R P B A 8 AB in plane U intersecting CD at point E

Given the points below as the vertices of a quadrilateral ABCD determine which sides segments ar parallel to each other and which are perpendicular Hint Draw the shape and name each of the four sides then find the slope of each A 2 5 B 6 3 C 5 1 D 7 2

Given the following figure prove that the m 14 31 degrees 156 20 14 35

The angle of elevation to a nearby tree from a point on the ground is measured to be 74 How tall is the tree if the point on the ground is 54 Feet from the bottom of the tree Round your answer to the nearest tenth of a foot if necessary

For an FCC structure select all reflections that can appear in the XRD pattern O 100 O 110 O 111 O 200 O 210 O 220 O 211 221

What is the maximum atomic scattering factor of Ti 00 O 10 O 22 O 29