Geometry Questions

4 If m 4 110 8 find a m S b m 8 EY l 1 2 3 4 5 6 7 8

7 With respect to b as a transversal for lines a and c a which angle corresponds to Z2 b which angle is the alternate interior angle for Z6 8 With respect to c as a transversal for lines a and b a which angle 12 5 6 10 9X11 12 Exercises 7 8 3 7 8 corresponds to 25 b which angle is the alternate exterior angle for 4 a b

Properties are some of the rules of mathematics which allow you to manipulate values and equations Most students are able to use the properties but do not realize their name nor why or how they work Match each property to each situation 3 x 7 3x 21 If a 40 then 3 8 a 15 5 0 0 If y 100 then y 10 90 5 0 5 Choose Zero Product Property Zero Sum Property Subtraction Property of Equality Distributive Property Division Property of Equality Choose Choose Choose

15 m with transversal t and 00 bisects LMON If m 1 112 find the following a m 2 b m 4 c m 5 d m MOQ 16 Given Find 17 Given Find e m Transversal t m 1 4x 2 m 6 4x 2 x and m 5 m n Transversal k m 3 x 3x m 6 x and m 4 x 4 x 5 EY m l 6 3 LO 1 2 M 4 At 5 0 7 I Exercises 15 16 6 N

In Exercises 27 to 35 complete the formal proof of each theorem 27 If two angles are complementary to the same angle ther these angles are congruent Given Prove 21 is complementary to 23 22 is complementary to 23 21 42

Given Find Given Find m n Transversal k m 3 x 3x m 6 x and m 4 m n Transversal k m 1 m 2 m 8 x 4 x 5 5x y 3x y 3x 5y x y and m 8 m 2 1 4 n 3 Exercises 17 19 6 LO 5 8 7

3 If two angles are supplementary to the same angle then these angles are congruent Given 1 is supplementary to 22 23 is supplementary to 22 21 43 Prove HINT See Exercise 27 for help 2 3

In Exercises 19 to 26 use the drawing in which AC intersects DB at point O A 19 If m 1 125 find m2 m 3 and m 4 20 If m 2 47 find m 1 m 3 and m 4 21 If m 1 3x 10 and m 3 4x 30 find x and m 1 D 3 O 1 2 4 B C

19 Sometimes symbols and abbreviations are used in place of a word or phrase What word or phrase is represented or abbreviated by each of the following b Zs c supp d rt a I e m 1

In Exercises 1 to 6 state the hypothesis H and the conclusion C for each statement 1 If a line segment is bisected then each of the equal segments has half the length of the original segment

2 If there were no understood restriction to lines in a plane in Theorem 1 4 3 the theorem would be false Explain why the following statement is false In space there is exactly one line perpendicular to a given line at any point on the line

3 Does the relation is perpendicular to have a reflexive prop erty consider line A symmetric property consider lines and m A transitive property consider lines l m and n

Is the following equation linear and con x 13y 3 17

lows The length of a line segment equals the sum of the lengths of its parts State a general conclusion regarding AB based on the following figure

Define a function f that represents a bucket s height d above the water in feet in terms of the angle of rotation measured in radians from the 3 o clock position Then use your function to find a bucket s height above the water when the angle of rotation is 4 radians from the 3 o clock position

Find the equation of the the line satisfying the given conditions Through 2 3 perpendicular to a second line y x O y x Oy x Oy x O y x

Solve 5 sin 5x 4 for the two smallest positive solutions A and B with A B A B Give your answers accurate to at least two decimal places

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