Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Chapter 5.CR, Problem 8CR

Find the value(s) of x in each proportion:

a) x 6 = 3 x c) 6 x + 4 = 2 x + 2
b) x − 5 3 = 2 x − 3 7 d) x + 3 5 = x + 5 7
e) x − 2 x − 5 = 2 x + 1 x − 1 g) x − 1 x + 2 = 10 3 x − 2
f) x ( x + 5 ) 4 x + 4 = 9 5 h) x + 7 2 = x + 2 x − 2
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Name: Tan Tong 16.5 Bonvicino - Period 5 1 Find the exact volume of a right hexagonal prism such that the base is a regular hexagon with a side length of 8 cm and whose distance between the two bases is 5 cm. Show all work. (4 pts) 83 tan 30°= Regular hexagon So length ~ 480 tango Cm Hexagon int angle =36016 8cm Angle bisec isper p bisect Side length 4 X=an 300 2 In the accompanying diagram of circle O, PA is tangent to the circle at A, PDC is a secant, diameter AEOC intersects chord BD at E, chords AB, BC, and DA are drawn, mDA = 46° and mBC is 32° more than mAB. If the radius of the circle is 8 cm, E is the midpoint of AO and the length of ED is 2 less than the length of BE, answer each of the following. Show all work. (a) m

18:36 G.C.A.2.ChordsSecantsandTa... จ 76 完成 2 In the accompanying diagram, AABC is inscribed in circle O, AP bisects BAC, PBD is tangent to circle O at B, and mZACB:m/CAB:m/ABC= 4:3:2 D B P F Find: mZABC, mBF, m/BEP, m/P, m/PBC ← 1 Ő
14:09 2/16 jmap.org 5G 66 In the accompanying diagram of circle O, diameters BD and AE, secants PAB and PDC, and chords BC and AD are drawn; mAD = 40; and mDC = 80. B E Find: mAB, m/BCD, m/BOE, m/P, m/PAD ← G.C.A.2.ChordsSecantsand Tangent s19.pdf (538 KB) + 4 保存... X

Chapter 5 Solutions

Elementary Geometry for College Students

Ch. 5.1 - In Exercises 1 to 4, give the ratios in simplified...Ch. 5.1 - In Exercises 1 to 4, give the ratios in simplified...Ch. 5.1 - In Exercises 1 to 4, give the ratios in simplified...Ch. 5.1 - In Exercises 1 to 4, give the ratios in simplified...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...
Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - In Exercises 5 to 14, find the value of x in each...Ch. 5.1 - Sarah ran the 300-m hurdles in 47.7 sec. In meters...Ch. 5.1 - Fran has been hired to sew the dance troupes...Ch. 5.1 - In Exercises 17 to 22, use proportions to solve...Ch. 5.1 - Prob. 18ECh. 5.1 - In Exercises 17 to 22, use proportions to solve...Ch. 5.1 - In Exercises 17 to 22, use proportions to solve...Ch. 5.1 - In Exercises 17 to 22, use proportions to solve...Ch. 5.1 - Prob. 22ECh. 5.1 - The salaries of a secretary, a salesperson, and a...Ch. 5.1 - The salaries of a school cook, custodian, and bus...Ch. 5.1 - If the measures of the angles of a quadrilateral...Ch. 5.1 - If the measures of the angles of a quadrilateral...Ch. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - If 1 in. equals 2.54 cm, use a proportion to...Ch. 5.1 - If 1 kg equals 2.2 lb, use a proportion to convert...Ch. 5.1 - For the quadrilaterals shown, MNWX=NPXY=PQYZ=MQWZ....Ch. 5.1 - Prob. 32ECh. 5.1 - Two numbers a and b are in the ratio 3:4. If the...Ch. 5.1 - Two numbers a and b are in the ratio 2:3. If both...Ch. 5.1 - If the ratio of the measure of the complement of...Ch. 5.1 - If the ratio of the measure of the complement of...Ch. 5.1 - On a blueprint, a 1-in. scale corresponds to 3 ft....Ch. 5.1 - Prob. 38ECh. 5.1 - Find a the exact length of an ideal rectangle with...Ch. 5.1 - Prove: If ab=cd where a, b, c and d are nonzero,...Ch. 5.1 - Prob. 41ECh. 5.2 - a What is true of any pair of corresponding angles...Ch. 5.2 - a Are any two quadrilaterals similar? b Are any...Ch. 5.2 - a Are any two regular pentagons similar? b Are any...Ch. 5.2 - a Are any two equilateral hexagons similar? b Are...Ch. 5.2 - In Exercises 5 and 6, refer to the drawing. a...Ch. 5.2 - In Exercises 5 and 6, refer to the drawing. a If...Ch. 5.2 - Prob. 7ECh. 5.2 - Given that rectangle ABCE is similar to rectangle...Ch. 5.2 - Given: MNPQRS,mM=56,mR=82,MN=9,QR=6,RS=7,MP=12...Ch. 5.2 - Given: ABCPRC,mA=67,PC=5,CR=12,PR=13,AB=26 Find: a...Ch. 5.2 - a Does the similarity relationship have a...Ch. 5.2 - Using the names of property from Exercise 11,...Ch. 5.2 - If the drawing, HJKFGK. If HK=6,KF=8, and HJ=4,...Ch. 5.2 - If the drawing, HJKFGK. If HK=6,KF=8, and FG=5,...Ch. 5.2 - Quadrilateral ABCD quadrilateral HJKL. If mA=55,...Ch. 5.2 - Quadrilateral ABCD quadrilateral HJKL. If...Ch. 5.2 - Quadrilateral ABCD quadrilateral HJKL. If...Ch. 5.2 - Quadrilateral ABCD quadrilateral HJKL. If...Ch. 5.2 - Quadrilateral ABCD quadrilateral HJKL. If...Ch. 5.2 - Quadrilateral ABCD quadrilateral HJKL. If...Ch. 5.2 - In Exercises 21 to 24, ADEABC. Given:...Ch. 5.2 - In Exercises 21 to 24, ADEABC. Given:...Ch. 5.2 - In Exercises 21 to 24, ADEABC. Given:...Ch. 5.2 - In Exercises 21 to 24, ADEABC. Given:...Ch. 5.2 - Pentagon ABCDE pentagon GHJKL not shown, AB=6, and...Ch. 5.2 - Quadrilateral MNPQ quadrilateral WXYZ not shown,...Ch. 5.2 - Prob. 27ECh. 5.2 - A technical drawing shows the 312 ft lengths of...Ch. 5.2 - In Exercises 29 to 32, use the fact that triangles...Ch. 5.2 - In Exercise 29 to 32, use the fact that triangles...Ch. 5.2 - In Exercise 29 to 32, use the fact that triangles...Ch. 5.2 - In Exercise 29 to 32, use the fact that triangles...Ch. 5.2 - In the drawing, ABDCEF with transversals l and m....Ch. 5.2 - In the drawing, ABDCEF. Suppose that transversals...Ch. 5.2 - Prob. 35ECh. 5.2 - Given RST, a second triangle (UVW) is constructed...Ch. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - For Exercises 39 to 40, use intuition to from a...Ch. 5.3 - What is the acronym that is used to represent each...Ch. 5.3 - Prob. 2ECh. 5.3 - Classify as true or false: a If the vertex angles...Ch. 5.3 - Classify as true or false: a If the midpoints of...Ch. 5.3 - In Exercises 5 to 8, name the method...Ch. 5.3 - In Exercises 5 to 8, name the method...Ch. 5.3 - In Exercises 5 to 8, name the method...Ch. 5.3 - In Exercises 5 to 8, name the method...Ch. 5.3 - Prob. 9ECh. 5.3 - In Exercises 9 to 12, name the method that...Ch. 5.3 - Prob. 11ECh. 5.3 - In Exercises 9 to 12, name the method that...Ch. 5.3 - In Exercises 13 to 16, provide the missing...Ch. 5.3 - In Exercises 13 to 16, provide the missing...Ch. 5.3 - In Exercises 13 to 16, provide the missing...Ch. 5.3 - In Exercises 13 to 16, provide the missing...Ch. 5.3 - In Exercises 17 to 24, complete each proof. Given:...Ch. 5.3 - In Exercises 17 to 24, complete each proof. Given:...Ch. 5.3 - Prob. 19ECh. 5.3 - In Exercises 17 to 24, complete each proof. Given:...Ch. 5.3 - Prob. 21ECh. 5.3 - In Exercises 17 to 24, complete each proof. Given:...Ch. 5.3 - In Exercises 17 to 24, complete each proof. Given:...Ch. 5.3 - Prob. 24ECh. 5.3 - In Exercises 25 to 28, ABCDBE Exercises 25-28...Ch. 5.3 - In Exercises 25 to 28, ABCDBE Exercises 25-28...Ch. 5.3 - In Exercises 25 to 28, ABCDBE Exercises 25-28...Ch. 5.3 - In Exercises 25 to 28, ABCDBE Exercises 25-28...Ch. 5.3 - CDECBA with CDEB. If CD=10,DA=8 and CE=6, find EB....Ch. 5.3 - CDECBA with CDEB. If CD=10,CA=16 and EB=12, find...Ch. 5.3 - ABFCBD with obtuse angles at vertices D and F as...Ch. 5.3 - ABFCBD with obtuse angles at vertices D and F as...Ch. 5.3 - In Exercise 33, provide a two-column proof....Ch. 5.3 - In Exercise 34, provide a paragraph proof. Given:...Ch. 5.3 - Use a two-column proof to prove the following...Ch. 5.3 - Prob. 36ECh. 5.3 - Use the result of Exercise 13 to do the following...Ch. 5.3 - Use the result of Exercise 13 to do the following...Ch. 5.3 - The distance across a pond is to be measured...Ch. 5.3 - In the figure, ABCADB. Find AB if AD=2 and DC=6.Ch. 5.3 - Prove that the altitude drawn to the hypotenuse of...Ch. 5.3 - Prove that the line segment joining the midpoints...Ch. 5.3 - Prob. 43ECh. 5.4 - By naming the vertices in order, state three...Ch. 5.4 - Use theorem 5.4.2 to form a proportion in which SV...Ch. 5.4 - Use theorem 5.4.3 to form a proportion in which RS...Ch. 5.4 - Use theorem 5.4.3 to form a proportion in which TS...Ch. 5.4 - Use theorem 5.4.2 to find RV if SV=6 and VT=8....Ch. 5.4 - Prob. 6ECh. 5.4 - Find the length of DF if: a DE=8 and EF=6. b DE=5...Ch. 5.4 - Find the length of DE if: a DF=13 and EF=5. b...Ch. 5.4 - Find EF if: a DF=17 and DE=15. b DF=12 and DE=82....Ch. 5.4 - Find DF if: a DE=12 and EF=5 b DF=12 and EF=6....Ch. 5.4 - Determine whether each triple (a,b,c) is a...Ch. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Determine the type of triangle represented if the...Ch. 5.4 - A guy wire 25 ft long supports an antenna at a...Ch. 5.4 - A strong wind holds a kite 30 ft above the earth...Ch. 5.4 - A boat is 6 m below the level of a pier and 12 m...Ch. 5.4 - A hot-air balloon is held in place by the ground...Ch. 5.4 - A drawbridge that is 104 ft in length is raised at...Ch. 5.4 - A drawbridge that is 136 ft in length is raised at...Ch. 5.4 - A rectangle has a width of 16 cm and a diagonal of...Ch. 5.4 - A right triangle has legs of lengths x and 2x2 and...Ch. 5.4 - A rectangle has base length x3, altitude length...Ch. 5.4 - The diagonals of a rhombus measure 6 m and 8 m....Ch. 5.4 - Each side of a rhombus measure 12 in. If one...Ch. 5.4 - An isosceles right triangle has a hypotenuse of...Ch. 5.4 - Prob. 27ECh. 5.4 - In right ABC with right C, AB=10 and BC=8. Find...Ch. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - In quadrilateral RSTU, RSST and UT diagonal RT. If...Ch. 5.4 - Prob. 34ECh. 5.4 - If a=p2q2,b=2pq and c=p2+q2, show that c2=a2+b2.Ch. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - When the rectangle in the accompanying drawing...Ch. 5.4 - A, C and F are three of the vertices of the cube...Ch. 5.4 - Prob. 40ECh. 5.4 - In the figure, square RSTV has its vertices on the...Ch. 5.4 - Prove that if (a,b,c) is a Pythagorean triple and...Ch. 5.4 - Use Figure 5.19 to prove Theorem 5.4.2. Theorem...Ch. 5.4 - Use Figures 5.20 and 5.21 to prove Lemma 5.4.3....Ch. 5.4 - Prob. 45ECh. 5.5 - For the 45-45-90 triangle shown, suppose that...Ch. 5.5 - For the 45-45-90 triangle shown, suppose that...Ch. 5.5 - For the 30-60-90 triangle shown, suppose that...Ch. 5.5 - For the 30-60-90 triangle shown, suppose that...Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - In Exercises 5 to 22, find the missing lengths....Ch. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - In Exercises 15 to 19, create drawings as needed....Ch. 5.5 - In Exercises15 to 19, create drawing as needed....Ch. 5.5 - Given: NQM with angles as shown in the drawing...Ch. 5.5 - Given: XYZ with angles as shown in the drawing...Ch. 5.5 - Given: Rhombus ABCD not shown in which diagonals...Ch. 5.5 - Prob. 23ECh. 5.5 - To unload groceries from a delivery truck at the...Ch. 5.5 - A jogger runs along two sides of an open...Ch. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - In Exercises 27 to 33, give both exact solutions...Ch. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - In Exercises 27 to 33, give both exact solutions...Ch. 5.5 - In Exercises 27 to 33, give both exact solutions...Ch. 5.5 - In Exercises 27 to 33, give both exact solutions...Ch. 5.5 - Note: Exercises preceded by an asterisk are of a...Ch. 5.5 - In regular hexagon ABCDEF, AB=6 inches. Find the...Ch. 5.5 - In regular hexagon ABCDEF, the length of AB is x...Ch. 5.5 - Prob. 37ECh. 5.5 - Diagonal EC separates pentagon ABCDE into square...Ch. 5.6 - Note: Exercises preceded by an asterisk are of a...Ch. 5.6 - Prob. 2ECh. 5.6 - Given that ABEF=BCFG=CDGH, are the following...Ch. 5.6 - Given that XYTS, are the following proportion...Ch. 5.6 - Given: l1l2l3l4,AB=5,BC=4,CD=3,EH=10 Find:...Ch. 5.6 - Given: l1l2l3l4,AB=7,BC=5,CD=4,EF=6 Find: FG,GH,EHCh. 5.6 - Given: l1l2l3,AB=4,BC=5,DE=x,EF=12x Find: x,DE,EFCh. 5.6 - Given: l1l2l3,AB=5,BC=x,DE=x2,EF=7 Find: x,BC,DECh. 5.6 - Given: DEBC,AD=5,DB=12,AE=7 Find: ECCh. 5.6 - Given: DEBC,AD=6,DB=10,AC=20 Find: ECCh. 5.6 - Prob. 11ECh. 5.6 - Given: DEBC,AD=5,DB=a+3,AE=a+1,EC=3(a1) Find:...Ch. 5.6 - Given: RW bisects SRT Do the following equalities...Ch. 5.6 - Given: RW bisects SRT Do the following equalities...Ch. 5.6 - Given: UT bisects WUV,WU=8,UV=12,WT=6 Find: TVCh. 5.6 - Given: UT bisects WUV,WU=9,UV=12,WV=9 Find: WTCh. 5.6 - Given: NQ bisects MNP,NP=MQ,QP=8,MN=12 Find: NPCh. 5.6 - Prob. 18ECh. 5.6 - Exercises 18 and 19 are based on a theorem not...Ch. 5.6 - Given: In ABC,AD bisects BAC AB=20 and AC=16 Find:...Ch. 5.6 - Prob. 21ECh. 5.6 - In ABC,mCAB=80,mACB=60,andABC=40. With the angle...Ch. 5.6 - In ABC,AC=5.3,BC=7.2 and BA=6.7. With angle...Ch. 5.6 - In right RST not shown with right S,RV bisects SRT...Ch. 5.6 - Given: RV bisects SRT, RS=x6,SV=3, RT=2x, and...Ch. 5.6 - Given: MR bisects NMP, MN=2x,NR=x, RP=x+1, and...Ch. 5.6 - Given point D in the interior of RST, which...Ch. 5.6 - In RST, suppose that RH,TG, and SK are medians....Ch. 5.6 - Given point D in the interior of RST, suppose that...Ch. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Given: RST, with XYRT and YZRS Prove: RXXS=ZTRZCh. 5.6 - Prob. 33ECh. 5.6 - Use Exercise 33 and the following drawing to...Ch. 5.6 - Use Theorem 5.6.3 to complete the proof of this...Ch. 5.6 - Prob. 36ECh. 5.6 - Given: ABC not shown is isosceles with...Ch. 5.6 - Given: RST with right RST; mR=30 and ST=6; RST is...Ch. 5.6 - Prob. 39ECh. 5.6 - Prob. 40ECh. 5.CR - Prob. 1CRCh. 5.CR - Prob. 2CRCh. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Find the values of x in each proportion: a x6=3x c...Ch. 5.CR - Use proportions to solve Review Exercises 9 to 11....Ch. 5.CR - Prob. 10CRCh. 5.CR - Prob. 11CRCh. 5.CR - The ratio of the measures of sides of a...Ch. 5.CR - Prob. 13CRCh. 5.CR - The length of the sides of a triangle are 6, 8 and...Ch. 5.CR - The ratio of the measure of the supplement of an...Ch. 5.CR - Prob. 16CRCh. 5.CR - Given: ABCD is a parallelogram. DB intersects AE...Ch. 5.CR - Prob. 18CRCh. 5.CR - Prob. 19CRCh. 5.CR - Prob. 20CRCh. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - Prob. 23CRCh. 5.CR - For Review Exercises 24 to 26, GJ bisects FGH...Ch. 5.CR - For Review Exercises 24 to 26, GJ bisects FGH...Ch. 5.CR - For Review Exercises 24 to 26, GJ bisects FGH...Ch. 5.CR - Given:...Ch. 5.CR - Prove that if a line bisects one side of a...Ch. 5.CR - Prove that the diagonals of a trapezoid divide...Ch. 5.CR - Given: ABCwithrightBACADBC...Ch. 5.CR - Given: ABCwithrightBACADBC...Ch. 5.CR - Prob. 32CRCh. 5.CR - Given:...Ch. 5.CR - Find the length of a diagonal of a square whose...Ch. 5.CR - Prob. 35CRCh. 5.CR - Find the length of a side of a rhombus whose...Ch. 5.CR - Find the length of an altitude of an equilateral...Ch. 5.CR - Prob. 38CRCh. 5.CR - The length of the three sides of a triangle are...Ch. 5.CR - Prob. 40CRCh. 5.CR - Prob. 41CRCh. 5.CR - Prob. 42CRCh. 5.CT - Reduce to its simplest form: a The ratio...Ch. 5.CT - Prob. 2CTCh. 5.CT - Prob. 3CTCh. 5.CT - Prob. 4CTCh. 5.CT - Prob. 5CTCh. 5.CT - In right triangle ABC,CD- is the altitude from C...Ch. 5.CT - Prob. 7CTCh. 5.CT - Prob. 8CTCh. 5.CT - Prob. 9CTCh. 5.CT - Prob. 10CTCh. 5.CT - In DEF,D is a right angle and m F=30. a Find DE if...Ch. 5.CT - Prob. 12CTCh. 5.CT - Prob. 13CTCh. 5.CT - For ABC, the three angle bisectors are shown. Find...Ch. 5.CT - Prob. 15CTCh. 5.CT - Prob. 16CTCh. 5.CT - In Exercises 16 and 17, complete the statements...
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