3D Geometry Questions and Answers

Classify each polygon formed by the intersection of a polyhedron and a plane a b circle O hexagon O pentagon Otriangle O square O circle O hexagon O pentagon O triangle square

a How many solids have faces that are hexagons b Name the solids from part a Select all that apply truncated tetrahedron cuboctahedron great rhombicosidodecahedron great rhombicuboctahedron icosidodecahedron snub dodecahedron small rhombicosidodecahedron small rhombicuboctahedron snub cube truncated cube truncated dodecahedron truncated icosahedron truncated octahedron

A credit card issuer offers an APR of 13 64 and compounds interest daily Which is it most likely to advertise its APR or its effective interest rate A Its APR because it s 0 97 less than its effective interest rate B Its APR because it s 0 97 greater than its effective interest rate C Its effective interest rate because it s 0 97 greater than its APR OD Its effective interest rate because it s 0 97 less than its APR

Addison put a 2290 item on layaway by making a 20 down payment and agreeing to pay 230 a month How many months sooner would she pay off the item if she increased her monthly payment to 310 A 14 months sooner B 8 months sooner C 6 months sooner D 2 months sooner

onvert the following degree measure to radian measure 15 315 radians Simplify your answer Type an integer or a fraction

Write your answer in simplified rationalized form U M or u

oval O A O B triangle O C circle D square

Alton had 725 for Medicare 3000 for state income tax and 3100 for Social Security deducted from his pay last year How much did Alton have deducted from his pay for FICA last year OA 3825 because FICA consists of Medicare and Social Security OB 3725 because FICA consists of Medicare and Social Security OC 3825 because FICA consists of Medicare and state income tax D 3725 because FICA consists of Medicare and state income tax

A computer hard disk starts from rest then speeds up with an angular acceleration of until it reaches its final angular speed of wf How many revolutions has the disk made at a time t seconds after it starts up T m Upload files Supported file formats PDF JPG GIF PNG CSV RTF TXT XPS ZIP Word Excel

6 3 2x 60 y

21 11 9 yd LA C 9 5 yd AB A 7b 9 5 11

3 Two diameters of a circle of radius 15 inches are drawn to make a central angle 48 A smaller circle is placed inside the bigger circle so that it is tangent to the bigger circle and to both diameters What is the radius of the smaller circle 48

ADEF has vertices D 8 4 E 2 6 and F 3 1 What are the vertices of the image after a dilation with a scale factor of 5 using the origin as the center of dilation

Sila In 1 2 State type of dilation and scale factor answer in simplest fraction for 2 12 in 12cm A 8 cm C 4 cm 8 cm B A A D D 9 in 6 in B C B 8 in

1 Does each set of given information guarantee that quadrilateral JKLM is a parallelogram Select yes or no for each situation A JN 25 cm JL 50 cm KN 13 cm KM 26 cm B ZMJL ZKLJ JM LK C JM JK KL LM D ZMJL ZMLJ ZKJL ZKLJ E AJKN ALMN O Yes OYes O Yes Yes O Yes O No O No O No O No O No M N K L

Find the volume blank 1 and total surface area blank 2 of this solid shown below 3 cm 4 cm Blank 1 Blank 2 5 cm 7 cm A A

x 4 m x x 2

2 7149 150 150 the volume 7 5556

Find the Surface Area and Volume of the following triangular prism 27 13 12 14 15 16

X 17 60

Find the area of the parallelogram with vertices A 1 1 4 B 0 3 9 C 1 0 7 and D 2 2 12 Area

Geometry 4 Point P is the centroid of AABC Find the indicated measurement a CD AP 3 mZ1 G AL 18 Find AP and PL 5 Find the missing length indicated SHOW WORK IF POSSIBLE a b 21 7 Complete the statement with or 1 AC DF A 24 118 E D m22 PL 20 H L 120 18 b BP 80 Find PL and BL PL 2 mZHGI S 3x 9 BL 4 KL MN B SR B x 7 K m IGJ G A H 9 1 9 30 21

19 yd 16 yd DO SUL TO 39 7 15 2 yd

28 m 28 m 22 1 m 3

Follow the guided instructions below to rotate the figure 270 clockwise about th origin Draw a circle centered at the center of rotation such that one of the vertices of the figure is on the circle 10 9 8 7 6 5 4 3 2 1 10 y 9 8 7 6 5 2 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 X

Next draw CD perpendicular to AB as shown in the next figure Label the red triangle as triangle 2 The blue triangle as triangle 3

Triangle 1 green is the original right triangle we started with Triangle 2 red is the other triangle formed by constructing CD Its right angle is angle D By comparing these two triangles we see that Therefore a cp Now let s complete the proof By adding the two equations we will get What do we notice about the side length p q So we can substitute p q for a b cp cq a b c p q By substitution we get a b c

as a zero 1 In Geogebra create the following function f x y 2sin x cos y which will plot the surface defined by the function and plot point A for the value in the function s domain The point should be a 3D point on the surface

6 Select a value for b such that a triangle with A 59 and a Ob 15 O b 24 O b 16 O b 11 Ob 17 14 has only one solution

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

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

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

In 7 10 Write a two column proof and mark triangles appropriately 7 Given PO SR PR SQ Prove APOR ASRO R Statement Reason

Find the reference number for t O 5TT 4 O T 4 O 5 TU 5TT 4

rating the inner quadrilateral He likes his new garden diagram better The ratio of each outer side to the corresponding inner side is 5 to 2 and the labels represent the lengths of the sides measured in inches Please note that images are not drawn to scale 4 What is the most descriptive name for the figure ABCD Explain your answer in at least one sentence The most descriptive name for the figure mangien e s cause it has y sides will be a Quadratteral 5 Find x 6 What is AB What is CD 5x 8 What is true of the diagonals of ABEF F 3x 3 D 5x 2x 5x E 7 What is the most descriptive name for ABEF Explain your answer in at least one sentence The most descriptive name for ABEF will be ause it has 4 equal sides and angles Square 9 What is the angle measure of each pair of base angles of ABCD How are these two angles related

Your Turn 1 Suppose a new regulation states that the maximum angle of a wheelchair ramp is 8 At least how long must the new ramp be Round to the nearest tenth of a foot Definition of sine ratio sin A sin 8 AC BC AC 2 3 AC AC sin 8 2 3 2 3 sin 8 AC 16 5 Substitution Property Multiplication Property Division Property Simplify C wall B 2 3 ft An A

Use a graphing utility to complete the table and graph the functions in the same viewing window Use both the table and the graph as evidence that yyz Round your answers to four decimal places Y cos x sin x tan x y2 sec x X 4 3 Y Y2 Verify the identity algebraically 4 8 Y cos x sin x tan x cos x cos x 1 cos x cos x X 5 3 X 5 8 6 3 6 8 7 3

5 Locate the points A 4 4 2 B 4 4 2 and C 4 4 2 using coordinat axes that you construct yourself Draw the corresponding rectangular box prism for each and label the coordinates of its vertices

7 Determine two other angles that have the same trigonometric ratios as each given angle a sin 60 b cos 230 d sin 150

se the drop down menus to explain if the two figures below are congruent similar or neither If the figures are similar state the scale factor Answer Attempt 1 out of 2 Figure BCDEF Figure BCDEF H 1 12 11 10 9 76543 C D 10 10 11 8 9 10 11 12 congruent to Figure GHIJK because rigid motions be used to map Figure BCDEF onto Figure GHIJK similar to Figure GHIJK because rigid motions and or dilations be used to map Figure BCDEF onto Figure

Solve the problem 34 A trough is to be made with an end of the dimensions shown The length of the trough is to be 16 feet long Only the angle 0 can be varied What value of 0 will maximize the trough s volume A 30 B 14 C 46 D 32 34

Find the length of a rectangular lot with a perimeter of 94 m if the length is 5 m more than the width O O O OA 26 m B 21 m OC 47 m OD 52 m

Write the equation of the circle in standard form Then identify its center and radius 9x 9y2 126x 72y 416 0 Center Radius

Find the point P at which the line intersects the plane x 8 7t y 4 7t z 7 10t 5x 4y 2z 13 The point P at which the line intersects the plane is 0 Simplify your answer Type an ordered triple

4 Almost everyone has played the rock paper scissors game at some point Two players face each other and at the count of 3 make a fist rock an extended hand palm down paper or a V with the index and middle fingers scissors The winner is determined by these rules rock smashes scissors paper covers rock and scissors cut paper If both players choose the same object then the game is a tie Suppose that Player 1 and Player 2 are both equally likely to choose rock paper or scissors a Give the probability model for this chance process b Find the probability that Player 1 wins the game on the first throw 5 Canada has two official languages English and French Choose a Canadian at random and ask What is your mother tongue Here is the distribution of responses combining many separate languages from the broad Asia Pacific region Language English French Asian Pacific Probability 0 63 0 22 0 06 a What probability should replace in the table Why Other b Find the probability that this Canadian s mother tongue is not English c What s the probability that a randomly chosen Canadian s mother tongue is Asian Pacific or Other

Four Thern 1 Use the Paragraph Proof of the Isosceles Triangle Theorem to complete a Theorem Hint Refer to the reasen bank below The first one is done for you Two Column Proof of the Isasceles Triangle Theorem AB a AC Prove S 5 Statements Draw AD the angle bisector of CAB LBAD LCAD AB AC 4 AD AD 5 BAD CAD 6 LB 2 C 1 2 3 Given Statements 1 Draw EH the angle bisector of ZFEG 2 LFEHLGEH 3 LF 2G 2 Complete a two column proof of the Converse of the Isosceles Triangle Theorem Hint Refer to the reason bank below Two Column Proof of the Converse of the Isosceles Triangle Theorem Prove EF EG LF LG A FEH BAGEH 6 EF EG Reason Bank CPCTC Corresponding Parts of Congruent Triangles are Congruent 1 Construction of angle bosector Given Reasons AAS Triangle Congruence en prost of the SAS Triangle Congruence B Reflexive Property of Congruence E Definition of angle bisecto Construction of angle bisector

HW 1 The interior angles of a triangle have measures of 2 What is the value of x in the figure below 55 25 and x Find the value of x D Complete problems 1 10 below for independent practice 3 Find the value of the missing angle using the Exterior Angle Theorem U 94 GT When you are finished check the solutions with your teacher 42 5 Find the value of the missing angle using the Exterior Angle Theorem E 105 155 V C Y 3x D 127 119 4 Find the value of the missing angle using the Exterior Angle Theorem S 53 W B 54 100 63 6 Find the value of the missing angle using the Exterior Angle Theorem T C V 80 U8 Camaldos que andag 0

Lesson 7 1 Interior and Exterior Angles Learning Goal I can prove the following theorems about triangles The measures of interior angles of a triangle sum to 180 Standard G CO C 10 EXPLORE Exploring Interior Angles in Polygons Read and complete the following adapted from Lesson 7 1 Show all your work interior angles The Triangle Angle Sum Theorem An interior angle is an angle formed by two sides of a polygon with a common vertex When we rearrange the interior angles of a triangle we find that they form a straight angle measuring 180 The sum of the angle measures of a triangle is 180 To determine the sum of the interior angles for any polygon you can consider how many triangles there are in other polygons If a convex po is broken up into triangles then the sum of the interior angles is the number of triangles times 180 For example by drawing the diagonal from a vertex of a quadrilateral you can form two triangles Since each triangle has an angle sum of 180 the quadrilateral must have an angle sum of 2 180 360 In each of the figures below how many triangles do you see Triangle Quadrilateral Pentagon Polygon Triangle Quadrilateral Pentagon Number of Sides 3 4 LAL Math Resources http bit ly L4LMath Hexagon Triangle s Triangle s Triangle s Triangle s Triangle s Triangle s For each polygon identify the number of sides the number of triangles and determine the angle sums of those triangles Remember that the sum of the angle measures of a triangle is 180 Number of Triangles 1 2 Heptagon Octagon Sum of Interior Angle Measures x 180 x 180 x 180 x 180

7 Given ZG ZT I is the midpoint of HV Prove ZH ZV H G T V Statement Reason

4 Given SP SR Q is the midpoint of PR Prove ZPSQ RSQ P R Statement Reason