Geometry Questions

12 Given Prove 3 2 Statements 1 41 23 2 and 4 21 22 23 24 Ls 2 and 3 are complementary Ls 1 and 4 are complementary 221 3 3 Ls 2 and 3 are complementary 6 42 and 24 2 4 5 mZ1 m24 90 PROOF 1 Reasons 2 If two Ls are then their measures are equal 3 4 The sum of the measures of complementary Zs is 90 5 6 If the sum of the mea sures of two angles is 90 than th

In Exercises 11 to 22 use the Given information to draw a conclusion based on the stated property or definition A Exercises 11 12 11 Given 12 Given 13 Given 14 Given 15 Given M 16 Given B A M B Segment Addition Postulate M is the midpoint of AB definition of midpoint I m 1 m 2 defini tion of angle bisector EG bisects LDEF defi nition of angle bisector Ls 1 and 2 are comple mentary definition of complementary angles 90 m 1 m2 definition of D E 1 2 G F Exercises 13 16

Solve sin x 0 42 on 0 x 2 There are two solutions A and B with A B A B

4 Given Prove O 1 2 3 4 A B C m AOB m 1 m BOC m 1 OB bisects LAOC Statements 1 PROOF Reasons 1 Given 2 Substitution 3 Angles with equal measures are congruent 4 If a ray divides an angle into two congruent angle then the ray bisects the angle

In Exercises 27 to 30 fill in the missing reasons for each geometric proof 27 Given Prove D E F on DF DE DF EF PROOF Statements 28 Given Prove 1 D E F on DF 2 DE EF DF 3 DE DF EF Statements 1 E is the midpoint of DF 2 DE EF 3 DE EF DF 4 DE DE DF 5 2 DE DF 6 DE DR E is the midpoint of DF DE DF 1 2 3 PROOF D E Exercises 27 28 1 2 3 4 5 Reasons Reasons F

36 Given Construct Straight LDEF A right angle with vertex at E HINT Use Construction 4 E

37 Given that a b and c 0 which is correct ac bc or ac bc

In Exercises 7 to 10 state the property or definition tha justifies the conclusion the then clause 7 Given that Ls 1 and 2 are supplementary then m 1 m22 180 R

28 For two complementary angles find an expression for the measure of the second angle if the measure of the first is a x b 3x 12 c 2x 5y

In Exercises 1 to 6 which property justifies the conclusion of the statement 1 If 2x 12 then x 6 2 If x x 12 then 2x 12

19 Given Find m RST 2x 10 m TSV x 6 m RSV 4 x 6 x and m RSV

15 Using variables x and y write an equation that expresses the fact that 1 and 2 are a complementary b vertical

13 LFAC and LCAD are adjacent and AF and AD are opposite rays What can you conclude regarding LFAC and LCAD

Find all angles that satisfy the equation 64 cos x 20 12 Use k for the number of rotations Separate your answers with a semicolon Degrees Radians Draw a picture of all angles between 0 and 360 in standar position and label the terminal points on the unit circle Draw the reference angles on the same picture not in standard position Label all angles in degrees and

A company is going to make a water tank in the shape of a cylinder As shown below the tank will have a height of 4 ft and a diameter of 10 ft The tank will be made from metal including its top and bottom Suppose the total cost of the metal will be 9325 80 How much will the metal cost per square foot Use 3 14 for and do not round your answer 10 ft 4 ft 0 X

rallelogram KLMN is shown below Give the coordinates of K L 0 s M 1 0 K N u 0 x K

Find the perimeter of the parallelogram with these vertices 6 4 1 4 1 5 6 5 Give an exact answer not a decimal approximation Simplify your answer as much as possible Scratch Area Not Part of Answer d 1 Perimeter 24 3 7 X

In the figure below KN and KL are tangent to the circle centered at O The segment NL passes through the center of the circle Given that KN 5 1 and NL 2 4 find NM N M 0 L NM X

A company manufactures aluminum mailboxes in the shape of a box with a half cylinder top The company will make 1960 mailboxes this week If each mailbox has dimensions as shown in the figure below how many square meters of aluminum will be needed to make these mailboxes In your calculations use the value 3 14 for and round up your answer to the next square meter 0 6 m 0 8 m 0 75 m 2 X

Compare the given measures by choosing or If there is not enough information select Cannot be determined If necessary you may learn what the markings on a figure indicate A X E K 15 Y 92 8 H 9 L 41 7 D B P 15 F 22 61 e 8 C G OAD CD Cannot be determined O mLF mLY O Cannot be determined KL QR Cannot be determined X 3

For each pair of solids determine whether they are similar If they are give the scale factor of Solid 1 to Solid 2 in simplest form Note The figures are not drawn to scale a The solids are right rectangular prisms Their lengths widths and heights are shown 1 1 15 cm Solid 1 15 cm Solid 1 16 cm 4 cm Solid 1 b The solids are right rectangular pyramids Their lengths widths and heights are shown 20 cm 5 cm 9 cm Solid 2 21 cm n 24 cm Solid 2 28 cm cm c The solids are right cylinders Their heights and base diameters are shown 9 cm 2 cm Solid 2 32 cm 8 cm 18 cm O Similar Scale factor O Not similar O Similar Scale factor Not similar O Similar Scale factor O Not similar

Write an equation of the circle with center 8 3 and radius 5 0 00 0 0

If we write the following complex number in standard form then b Your answers here have to be simplified so that the 2 131 2 13i a bi

Numerically estimate the absolute extrema of f x 10x 30x cos x on 9 0 Round your answers to four decimal places The absolute select The absolute select is approximately 2 8051 is approximately 9

A designer builds a model of a bicycle The finished model is exactly the same shape as the original but smaller The scale factor is 2 9 a Find the ratio of the surface area of the model to the surface area of the original b Find the ratio of the height of the model to the height of the original c Find the ratio of the volume of the model to the volume of the original Write these ratios in the format m n surface area height volume X

Here are the endpoints of the segments JK MN and PQ J 4 5 K 7 7 M 1 6 N 1 3 P 3 0 Q 5 3 Follow the directions below a Find the length of each segment Give an exact answer not a decimal approximation JK MN 0 PQ b Check all statements that are true below OJK MN OJK PQ OMNPQ None of these are true 4 9 16 9 8 08 X S

Determine if the statement is true or false The function defined by g x 3 x 3 2x 1 touches but does not cross the x axis at True False X at 1 0 5

Find x Round your answer to the nearest tenth of a degree 18 11 X 0

The empty gas tank of a truck needs to be completely filled The tank is shaped like a cylinder that is 3 5 ft long with a diameter of 2 4 ft Suppose gas is poured into the tank at a rate of 1 7 ft per minute How many minutes does it take to fill the empty tank Use the value 3 14 for it and round your answer to the nearest minute Do not round any intermediate computations minute s X

A company rents water tanks shaped like cylinders Each tank has a diameter of 12 feet and a height of 3 feet The cost is 2 per cubic foot How much does it cost to rent one water tank Use 3 14 for and do not round your answer

The radius of a cylindrical construction pipe is 2 5 ft If the pipe is 22 ft long what is its volume Use the value 3 14 for and round your answer to the nearest whole number Be sure to include the correct unit in your answer 22 ft 2 5 ft 1

For the following right triangle find the side length x X

In the figure below n g Find the values of x and y 5y 74 84 to X 11 11 y 0

The two triangles below are similar Also mLH 20 and mI 100 as shown below Find mLX mLY and mLZ Assume the triangles are accurately drawn G I 100 m2x 0 m 2 Y 20 H X Z

Find an equation for the graph Type the equation of the given graph in the form y Asin Bx or y A cos Bx D otion Ico intogors or fractions for any numbers in the equation Simplify your answer 3 TU 2 JTC 5 3 14 IT

Suppose that AB AC AD AE and AF are coplanar F A B D E

Plot the complex number Then write the complex number in polar form Express the argument in degrees 9 9i Plot the complex number on the complex plane to the right AImaginary Real

27 Using the number line provided name the point that a is the midpoint of AE b is the endpoint of a segment of length 4 if the other endpoint is point G has a distance from B equal to 3 AC A E F 3 B 2 C 1 D 0 1 2 G 3 H 4

What relationship if any exists between two angles a with equal measures b that have the same vertex and a common side between them

31 Given Construct AB as shown in the figure PQ on line n so that PQ 3 AB A B

20 Suppose that point C lies in plane X and point D lies in plane X What can you conclude regarding CD

9 Name three points that appear to be a collinear b noncollinear 0 How many lines can be drawn through I a point A b points A and B c points A B and C d points A B and D A C Exercis

17 Given Find AM AB x and AB 2x 1 MB 3x 2 and 6x 4

4 Classify as true or false a AB BC AD CD AB CD AC b AD c AD A M B C D d AB BC CD AD e AB BC I

16 Given Find M is the midpoint of AB AM 2 x 1 and MB 3 x 2 x and AB

41 Find m ABC if m 1 42 and m 2 29 42 Find m 1 if m ABC 68 and m 1 m 2 43 Find x if m 2 x m 1 2x 3 and m ABC 72 A 1 B 2 D C Exercises 41 44

25 The sides of the pair of angles are parallel Are 21 and 22 congruent 2

37 Find x if AB x BC x 3 and AC 21

39 LABC is a straight angle Using your protractor you can show that m 1 m 2 180 Find m 1 if m2 56 A 1 2 B Exercises 39 40 40 Find m 1 if m 1 D C 2x and m 2 X UNT Son Exarcica 39

34 An angle is bisected if its two parts have the same measure Use three letters to name the angle that is bisected A B 10 10 15 C D F