2D Geometry Questions and Answers

10 If a point is chosen at random in the solid below what is the probability that it lies within the hemisphere 11 If a point in the cylinder below is chosen at random what is the probabilitiy that it lies within the shaded region T10in1 14 in

MNOP is a parallelogram Select the true statements used to prove that opposite angles of a parallelogram are congruent Select two M Show your work here P B Y 8 N 28 28 because same side interior angles are congruent when a transversal crosses parallel lines O La Z8 because alternate interior angles are congruent when a transversal crosses parallel lines AMNP AOPN by the angle side angle congruence criterion AMNPAOPN by the side angle side congruence criterion Za Zy because same side interior angles are congruent

KLMN is a rectangle Select the statements used to prove that diagonals are congruent Select two N K Show your work here O AKLN ALKM by the side angle side criterion OAKLN ALMN by the side angle side criterion OAKLNAKLM by the angle side angle criterion Adjacent sides of a parallelogram are congruent M L

Select the statement used to prove that KL MN K N 24 Show your work here 15 15 L OAKLO AMNO by the ASA criterion O AKLNAMNL by the SAS criterion 24 OAKLO AMNO by the SAS criterion M

Find each area occupied by the sprouts between the concentric circles Use 3 14 for T 18 4 in 150 6 in 19 15 cm 100 5 cm

A right circular cylinder is to be inscribed into a sphere of radius 9 Find the dimensions of the cylinder which has maximum volume What is the volume

Proots Practice CONGRUENT TRIANGLE PROOFS practice Given PQI RS SP II QR Prove ARSP APQR Statements LPQRS 2 SPQR 3 RPS PRQ and PRS RPQ 4RP PR 5 ARSP APOR Reasons Given Given Reflexive L 2 3 5 Prop

Congruent Triangle Proofs Practice 2 CONGRUENT TRIANGLE PROOFS Given XV XZ V Z Prove W ZY Statements XVEXZ 2 2V 2Z 3 5 W LY 4 Reasons Given 12 Given 3 Vertical angles are congruent 4 N 5 C PCT C

1 How many midsegments does a triangle have A trapezoid 2 What is the perimeter of ATOP P 8 T 20 0 10 3 x y 60 40 4 z 65 Constructio for Exercises

5 What is the perimeter of ATEN T 9 U 23 N 8 6 m P In 73 36 cm 48 cm 771 510 7 q 13 24

Using the graph below point B is represented by 90 0

Using the graph below point A is represented by m U D

Which coordinate s represent the same point as 3 in a polar coordinate system Select one or more O a 3 7 b 3 5 OC 3 7 O d 3 13

Each large cookie is 5 6 oz and each small cookie is 4 9 oz What is the total weight of 2 large cookies and 1 small cookie 2 1 9 oz 3 1 9 oz 2 oz 3 oz

An aquarium has exhibits that feature different marine animals 5 8 of the staff are male 5 12 of the staff works part time at the aquarium What fraction of the staff is female

In a piping system the HGL is located a distance p y above the datum of the pipe Select one O True O False

Which expressions represent the statement divide the difference of 27 and 3 by the difference of 16 and 4 3 27 3 16 4 27 3 16 4 27 3 16 4 0 27 3 16 4 27 16 4 3 16 4

Robert says the expressions 2 3X7 and 2 3 x 7 have the same value Is Robert correct Explain your answer and evaluate each expression

Ella babysits 3 hours each day for 4 days On the fifth day she babysits for 6 hours Which expression represents how many hours Ella babysits altogeth 4 3 6 4x 3 6 3x 4 6 3x4 6

A parallelogram is a quadrilateral four sided figure with two pairs of parallel opposite sides A rhombus is a parallelogram all of whose sides have the same length A Explain how two nonzero and nonparallel vectors in R2 two dimensional space can be used to determine a parallelogram B Explain how one nonzero vector in R can be used to determine a rhombus with one side on the z axis C Draw a picture of the rhombus with one side on the ar axis determined by the vector 5 2 Then show that the diagonals of this rhombus intersect at a right angle D Do the diagonals of any rhombus intersect at a right angle Explain

6 Circle O has a diameter of length 16 A point Cis located outside of the circle such that it lies 12 units from the circle s center What would the length of a segment drawn from C tangent to circle O be Hint Draw a picture

be Hint Draw a picture What would the length of a segment drawn from C tangent to circle O Challenge 7 In the diagram shown on circle A segment CD is tangent to the circle at point D If CD 23 and CA 28 then which of the following is closest to mzC 1 22 3 31 2 26 4 35 O

The lengths of the diagonals of a rhombus are 10 and 24 Find the perimeter of the rhombus OA 48 OB 52 O C 13 O D 40

If a ray QT bisects RQS what would be the measure of one of the resulting angles P measure 3x 5 R x 1 S

Two segments are shown in the figure below 9 8 D 9 8 7 6 5 3 2 1 3 2 1 0 1 2 3 4 5 6 7 8 9 B 67 If segments were drawn from D to a Point C and from B to a Point C what coordinates of Poi BEST represent a vertex of Rhombus ABCD O A 2 9 O B 2 0 O C 2 1

Use the diagram shown 3 Which theorem or postulate justifies the statement below Angle 2 is congruent to angle 4 O A Congruent Supplements Theorem O B Linear Pairs Theorem OC Angle Addition Postulate OD Vertical Angles Theorem

If a number is an integer then it is either positive or negative Which is a counterexample for the conditional OA 0 OB 1 O C 111 OD 2

Trapezoid LMNO is shown below OB 9 4 O C 8 L O D 164 9x 64 Z 5x 4 M 20x 24 What must be the value of x to prove trapezoid LMNO is an isosceles trapezoid O A 15 4x 12 N

If DM 25 what is the value of r D r 2 OA 12 OB 13 O C 14 D 15 G 2r 13 M

Parallelogram ABCD is shown below What is the value of x D OA 8 OB 2 O C 30 O D T 1 2 A 3x 6 5x 10 E C B

In quadrilateral DEFG below DG is parallel to EF What is the measure of ZF O A 95 OB 85 O C 105 D x 10 to

Given Quadrilateral RSTW which conditions are sufficient to prove that RSTW is a rectangle R W OA RT bisects SW and ST RT OB RS TW ST RW C ST RW RS I ST OD SR RW and RT is the perpendicular bisector of SW

An exterior angle in a regular polygon measures 14 4 What is the name of the polygon O A 25 gon O B doecagon OC 20 gon O D decagon

1 In each triangle name the side a a 2 Calculate the Tan A and Tan B in each triangle 3 Calculate a 1 5 cm a 4 Calculate the value of x 4 cm 3 7 cm E adjacent Z F Y B b B Tan 35 55 b 18 cm 12 cm b opposite Z 13 4 cm b Tan 71 c Tan d Tan 90

What is the measure of an exterior angle of a regular polygon with 5 si OA 45 OB 72 O C 85 O D 60

An exterior angle of a regular polygon measures 40 How many sides does the polygon have O A 12 O B 9 O C 8 O D 10

Question 1 of 12 1 point Question Attempt 6 of Unlimited Figure A Figure B 3 in 3 in 3 in L 3 in a Which figures are squares Mark all that apply Figure A Figure B b Which figures are parallelograms Mark all that apply Figure A Figure B c Which figures are rectangles Mark all that apply Figure A 3 in Figure B Figure C Figure C Figure C 5 in 5 in 3 in None of the figures 4 None of the figures None of the figures 5 in 5 in Figure C X 4 in 4 in

In the rectangle below FH 6x 6 EI 9 and m2 IFG 29 Find the value of x and mLIGH E F X m LIGH 15 151 X

Suppose you need to pump air into a volleyball that is completely deflated The deflated volleyball weighs 20 81 ounces After being inflated the ball weighs 21 06 ounces The volleyball has a diameter of 0 07 feet What is the density of air in the ball Assume the ball is perfectly spherical Round your answer to the nearest integer Show your work here

11 5 3 Practice In Exercises 1 10 graph the function Determine when the function is positive negative increasing or decreasing Then describe the end behavior of the function See Example 1 1 y 8 x 3 y 4 V I 2 y V4x 5 h x x 4 9 m x 2 x 4 11 WITH CalcChat AND CalcView X 6 p x 7 f x x 8 16 g x 5Vx 10 n x x 2 4 y cises 11 18 graph the function Compare the graph to the graph of f x x See Example 2 Vx 12 x 2x 13 h x x 3 14 g x x 8 1 8 g x x 1 17 m x x 6 18 n x V

db are A a 68 b parallel What is the measure of 27 if 22 measures 6

Find the volume of the composite solid which is a hemisphere atop a cylinder 6

V s cut by the transversal line t Which THREE angl

D The quadrilateral shown is a rhombus If AB 17 and AE 8 what is the meas x

The quadrilateral shown is a parallelogram If m ZADC 12 A 55

The quadrilateral shown is a rectangle What is mZZVW x A 61 x B 39 C 119 W Z 61 V

x The figure is a parallelogram The mZACD 4x 4 and mZABD 6x 14 Find mZACD x A 9 B 40 C

x The quadrilateral shown is a rhombus If BC 41 and BE 40 what is the measure of AE A 15 4x B 12 C 9 D D 18 E C

x The quadrilateral shown is a rhombus What is m 24 x A 58 4

If ABCD is a square and AB 10 what is the meas 1414