Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Textbook Question
Chapter 8.5, Problem 38E
Use the results from Exercises 36 and 37 to find the exact length of the radius of the inscribed
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b)
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The diagram below shows a light plank balanced on two supports, A and B.
Weights of 50 N, 25 N and 30N are placed on the plank as shown. X and Y
are the normal reactions to the supports.
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Y
50 N
25 N
30 N
5 cm
15 cm
15 cm
15 cm
20 cm
20 cm
A
B
Solve for x
1) Given: MNPQ is a parallelogram with MP 1 NQ.
Prove: MNPQ is a rhombus.
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Reason
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Chapter 8 Solutions
Elementary Geometry for College Students
Ch. 8.1 - Suppose that two triangles have equal areas. Are...Ch. 8.1 - The area of the square is 12, and the area of the...Ch. 8.1 - Consider the information in Exercise 2, but...Ch. 8.1 - If MNPQ is a rhombus, which formula from this...Ch. 8.1 - In rhombus MNPQ, how does the length of the...Ch. 8.1 - When the diagonals of rhombus MNPQ are drawn, how...Ch. 8.1 - Prob. 7ECh. 8.1 - Are ABC and DEF congruent? Exercises 7, 8Ch. 8.1 - Prob. 9ECh. 8.1 - In Exercises 9 to 18, find the areas of the...
Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - Prob. 12ECh. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - In Exercises 9 to 18, find the areas of the...Ch. 8.1 - Prob. 18ECh. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - Prob. 20ECh. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - In Exercises 19 to 22, find the area of the shaded...Ch. 8.1 - A triangular corner of a store has been roped off...Ch. 8.1 - Carpeting is to be purchased for the family room...Ch. 8.1 - The exterior wall the gabled end of the house...Ch. 8.1 - The roof of the house shown needs to be...Ch. 8.1 - A beach tent is designed so that one side is open....Ch. 8.1 - Gary and Carolyn plan to build the deck shown. a...Ch. 8.1 - A square yard is a square with sides 1 yard in...Ch. 8.1 - The following problem is based on this theorem: A...Ch. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - In Exercises 34 to 36, provide paragraph proofs....Ch. 8.1 - In Exercises 34 to 36, provide paragraph proofs....Ch. 8.1 - In Exercises 34 to 36, provide paragraph proofs....Ch. 8.1 - Given: The area of right ABC not shown is 40in2....Ch. 8.1 - The lengths of the legs of a right triangle are...Ch. 8.1 - Given: ABC, whose sides are 13 in., 14 in., and 15...Ch. 8.1 - Prob. 40ECh. 8.1 - If the length of the base of a rectangle is...Ch. 8.1 - If the length of the base of a rectangle is...Ch. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - The algebra method of FOIL multiplication is...Ch. 8.1 - Use the square configuration to complete the...Ch. 8.1 - In Exercises 47 to 50, use the fact that the area...Ch. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - In Exercises 47 to 50, use the fact that the area...Ch. 8.1 - The area of a rectangle is 48in2. Where x is the...Ch. 8.1 - The perimeter of the rectangle is 32 cm. Where x...Ch. 8.1 - Square DEFG is inscribed in right ABC, as shown....Ch. 8.1 - TV bisects STR of STR. ST=6 and TR=9. If the area...Ch. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 1 to 8, find the perimeter of each...Ch. 8.2 - In Exercises 9 and 10, use Herons Formula. Find...Ch. 8.2 - Prob. 10ECh. 8.2 - For Exercises 11 and 12, use Brahmaguptas Formula....Ch. 8.2 - For Exercises 11 and 12, use Brahmaguptas Formula....Ch. 8.2 - Prob. 13ECh. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - In Exercises 13 to 18, find the area of the given...Ch. 8.2 - Prob. 18ECh. 8.2 - In a triangle of perimeter 76 in., the length of...Ch. 8.2 - In a triangle whose area is 72 in2, the base has a...Ch. 8.2 - A trapezoid has an area of 96 cm2. If the altitude...Ch. 8.2 - The numerical difference between the area of a...Ch. 8.2 - Prob. 23ECh. 8.2 - Find the ratio A1A2 of the areas of two similar...Ch. 8.2 - In Exercises 25 and 26, give a paragraph form of...Ch. 8.2 - In Exercises 25 and 26, give a paragraph form of...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - In Exercises 27 to 30, find the area of the figure...Ch. 8.2 - Mary Frances has a rectangular garden plot that...Ch. 8.2 - Prob. 32ECh. 8.2 - Farmer Watson wishes to fence a rectangular plot...Ch. 8.2 - The farmer in Exercise 33 has decided to take the...Ch. 8.2 - Prob. 35ECh. 8.2 - Find the perimeter of the room in Exercise 35.Ch. 8.2 - Examine several rectangles, each with a perimeter...Ch. 8.2 - Examine several rectangles, each with an area of...Ch. 8.2 - Square RSTV is inscribed in square WXYZ, as shown....Ch. 8.2 - Square RSTV is inscribed in square WXYZ, as shown....Ch. 8.2 - For Exercises 41 and 42, the sides of square ABCD...Ch. 8.2 - For Exercises 41 and 42, the sides of square ABCD...Ch. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - For Exercises 45 and 46, use this information: Let...Ch. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - For Exercises 48 and 49, use the formula found in...Ch. 8.2 - Prove that the area of a square whose diagonal has...Ch. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - The shaded region is that of a trapezoid....Ch. 8.2 - Trapezoid ABCD not shown is inscribed in O so that...Ch. 8.2 - Each side of square RSTV has length 8. Point W...Ch. 8.2 - For the cyclic quadrilateral MNPQ, the sides have...Ch. 8.3 - Find the area of a square with a sides of length...Ch. 8.3 - Find the area of a square with a a perimeter of...Ch. 8.3 - Find the area of an equilateral triangle with a...Ch. 8.3 - Find the area of an equiangular triangle with a a...Ch. 8.3 - In a regular polygon, each central angle measures...Ch. 8.3 - In a regular polygon, each interior angle measures...Ch. 8.3 - For a regular hexagon, the length of the apothem...Ch. 8.3 - For a regular hexagon, the length of the radius is...Ch. 8.3 - In a particular type of regular polygon, the...Ch. 8.3 - In a particular type of regular polygon, the...Ch. 8.3 - Prob. 11ECh. 8.3 - If the area (A=12aP) and the perimeter of a...Ch. 8.3 - Find the area of a square with apothem a = 3.2 cm...Ch. 8.3 - Find the area of an equilateral triangle with...Ch. 8.3 - Find the area of an equilateral triangle with...Ch. 8.3 - Find the area of a square with apothem a = 8.2 ft...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - Prob. 21ECh. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - In Exercises 17 to 30, use the formula A=12aP to...Ch. 8.3 - Find the ratio of the area of a square...Ch. 8.3 - Given regular hexagon ABCDEF with each side of the...Ch. 8.3 - Given a regular octagon RSTUVWXY with each side of...Ch. 8.3 - Regular octagon ABCDEFGH is inscribed in a circle...Ch. 8.3 - Given regular pentagon RSTVQ and equilateral...Ch. 8.3 - Consider regular pentagon RSTVQ not shown. Given...Ch. 8.3 - Prob. 37ECh. 8.3 - The length of each side of a regular hexagon...Ch. 8.4 - Find the exact circumference and area of a circle...Ch. 8.4 - Find the exact circumference and area of a circle...Ch. 8.4 - Prob. 3ECh. 8.4 - Find the approximate circumference and area of a...Ch. 8.4 - Find the exact lengths of the radius and the...Ch. 8.4 - Find the approximate lengths of the radius and the...Ch. 8.4 - Find the exact lengths of the radius and the...Ch. 8.4 - Find the exact length of the radius and the exact...Ch. 8.4 - Find exactly lAB, where AB refers to the minor arc...Ch. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Use your calculator value of to find the...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - A rectangle has an area of 36 in2. What is the...Ch. 8.4 - The legs of an isosceles triangle each measure 10...Ch. 8.4 - Two sides of a triangle measure 5 in and 7 in....Ch. 8.4 - Let N be any point on side BC of the right...Ch. 8.4 - What is the limit of mRTS if T lies in the...Ch. 8.4 - In exercises 23-26, find the exact areas of shaded...Ch. 8.4 - In exercises 23-26, find the exact areas of shaded...Ch. 8.4 - In exercises 23-26, find the exact areas of shaded...Ch. 8.4 - In exercises 23-26, find the exact areas of the...Ch. 8.4 - In Exercises 27 and 28, use your calculator value...Ch. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - The ratio of the circumferences of two circles is...Ch. 8.4 - Given concentric circles with radii of lengths R...Ch. 8.4 - Prob. 32ECh. 8.4 - The radii of two concentric circles differ in...Ch. 8.4 - Prob. 34ECh. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - In Exercises 34-44, use your calculator value of ...Ch. 8.4 - Prob. 44ECh. 8.4 - The diameter of a carousel merry-go-round is 30ft....Ch. 8.4 - A tabletop is semicircular when its three...Ch. 8.4 - Given that the length of each side of a rhombus is...Ch. 8.5 - Given O with radii OA- and OB- and chord AB-....Ch. 8.5 - Prob. 2ECh. 8.5 - In the semicircular region shaded DQ=6". a Find...Ch. 8.5 - For the semicircular region of Exercise 3, the...Ch. 8.5 - In the circle, the radius length is 10 in. and the...Ch. 8.5 - If the area of the circle is 360 in2, what is the...Ch. 8.5 - If the area of 1200 sector is 50 cm2, what is the...Ch. 8.5 - If the area of the 1200 sector is 40 cm2 and the...Ch. 8.5 - Prob. 9ECh. 8.5 - Suppose a circle of radius r is inscribed in a...Ch. 8.5 - Find the perimeter of a segment of a circle whose...Ch. 8.5 - Prob. 12ECh. 8.5 - A circle is inscribed in a triangle having sides...Ch. 8.5 - A circle is inscribed in a triangle having sides...Ch. 8.5 - A triangle with sides of lengths 3 in., 4 in., and...Ch. 8.5 - The approximate area of a triangle with sides of...Ch. 8.5 - Find the exact perimeter and area of the sector...Ch. 8.5 - Find the exact perimeter and area of the sector...Ch. 8.5 - Prob. 19ECh. 8.5 - Find the approximate area of the sector shown....Ch. 8.5 - Find the exact perimeter and area of the segment...Ch. 8.5 - Prob. 22ECh. 8.5 - In Exercises 23 and 24, find the exact areas of...Ch. 8.5 - In Exercises 23 and 24, find the exact areas of...Ch. 8.5 - Assuming that the exact area of a sector...Ch. 8.5 - Prob. 26ECh. 8.5 - A circle can be inscribed in the trapezoid shown....Ch. 8.5 - Prob. 28ECh. 8.5 - In a circle whose radius has length 12 m, the...Ch. 8.5 - At the Pizza Dude restaurant, a 12-in. pizza costs...Ch. 8.5 - Prob. 31ECh. 8.5 - Determine a formula for the area of the shaded...Ch. 8.5 - Determine a formula for the area of the shaded...Ch. 8.5 - Find a formula for the area of the shaded region,...Ch. 8.5 - A company logo on the side of a building shows an...Ch. 8.5 - Prob. 36ECh. 8.5 - Prob. 37ECh. 8.5 - Use the results from Exercises 36 and 37 to find...Ch. 8.5 - Prob. 39ECh. 8.5 - Three pipes, each of radius length 4 in., are...Ch. 8.5 - A windshield wiper rotates through a 1200 angle as...Ch. 8.5 - A goat is tethered to a barn by a 12-ft chain. If...Ch. 8.5 - Prob. 43ECh. 8.5 - In ABC,mC=90 and mB=60. If AB=12 in., find the...Ch. 8.5 - A triangle has sides of lengths 6 cm, 8 cm and 10...Ch. 8.CR - For the Review Exercises, give an exact answer...Ch. 8.CR - For the Review Exercises, give an exact answer...Ch. 8.CR - Prob. 3CRCh. 8.CR - Prob. 4CRCh. 8.CR - Prob. 5CRCh. 8.CR - Given: Trapezoid ABCD, with...Ch. 8.CR - Given: Trapezoid ABCD, with AB=6andBC=8,ABCD Find:...Ch. 8.CR - Find the area and the perimeter of a rhombus whose...Ch. 8.CR - Tom Morrow wants to buy some fertilizer for his...Ch. 8.CR - Alices mother wants to wallpaper two adjacent...Ch. 8.CR - Given: Isosceles trapezoid ABCD Equilateral FBC...Ch. 8.CR - Given: Kite ABCD withAB=10BC=17,andBD=16 Find:...Ch. 8.CR - One side of a rectangle is 2 cm longer than a...Ch. 8.CR - One side of a triangle is 10 cm longer than a...Ch. 8.CR - Prob. 15CRCh. 8.CR - Find the area of an equilateral triangle if each...Ch. 8.CR - If AC is a diameter of O, find the area of the...Ch. 8.CR - Prob. 18CRCh. 8.CR - Find the area of a regular hexagon, each of whose...Ch. 8.CR - Prob. 20CRCh. 8.CR - Prob. 21CRCh. 8.CR - Prob. 22CRCh. 8.CR - Can a circle be circumscribed about each of the...Ch. 8.CR - Can a circle be inscribed in each of the following...Ch. 8.CR - Prob. 25CRCh. 8.CR - The Turners want to install outdoor carpet around...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - Find the exact areas of the shaded regions in...Ch. 8.CR - The arc of a sector measures 40. Find the exact...Ch. 8.CR - The circumference of a circle is 66 ft. aFind the...Ch. 8.CR - A circle has an exact area of 27ft2. aWhat is the...Ch. 8.CR - Prob. 35CRCh. 8.CR - Prob. 36CRCh. 8.CR - Prove that the area of a circle circumscribed...Ch. 8.CR - Prove that if semicircles are constructed on each...Ch. 8.CR - Jeff and Helen want to carpet their family room,...Ch. 8.CR - Prob. 40CRCh. 8.CT - Complete each statement. a Given that the length...Ch. 8.CT - Give each formula. a The formula for the area of a...Ch. 8.CT - Prob. 3CTCh. 8.CT - If the area of rectangle ABCD is 46 cm2, find the...Ch. 8.CT - Prob. 5CTCh. 8.CT - Prob. 6CTCh. 8.CT - Prob. 7CTCh. 8.CT - In trapezoid ABCD, AB=7 ft and DC=13 ft. If the...Ch. 8.CT - Prob. 9CTCh. 8.CT - Prob. 10CTCh. 8.CT - Prob. 11CTCh. 8.CT - Prob. 12CTCh. 8.CT - Prob. 13CTCh. 8.CT - Find the exact area of the 1350 sector shown. _Ch. 8.CT - Prob. 15CTCh. 8.CT - Prob. 16CTCh. 8.CT - Pascual is remodeling a house and plans a complete...
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- 1) Given: MNPQ is a parallelogram with MP 1 NQ. Prove: MNPQ is a rhombus. Statement Reason M R Parrow_forward4) Find a proposition with three variables p, q, and r that is never true. 5) Determine whether this proposition is a tautology using propositional equivalence and laws of logic: ((p (bv (bL ← →¬p [1 6) Explain why the negation of "Some students in my class use e-mail” is not "Some students in my class do not use e-mail".arrow_forwardMilgram lemma B) Consider Show that -Au= f in a u=0 on on llu-ulls Chllullz 02 Prove that Where ||ul| = a(u, u) = vu. Vu dx + fonu.u ds Q3: Let V = H' (2), a(u,v) = CR, a(u,v) = (f,v) where Vu. Vv dx + Ja cuv dx and ||u|=|||| Show that a(u, v) is V-ellipiticly and continuity.arrow_forward
- 7) Is the following statement True or False: AU BUA = Ā. Justify your answer. 8) Suppose g: A → B and f: B → C where A = {2,3,6,8}, and g and f are defined by g = {a, b, c, d}, B = {1,2,3}, C = {(a,2), (b,1), (c, 3), (d, 2)} and f = {(1,8),(2,3), (3,2)}. Find fog, gof and f−¹. 9) Verify that a₁ = 7(3") -π is a solution to the recurrence relation an = an 4an-1 -3an-2arrow_forward1) Find the prime factorization of 111111. 2) Find (-88 mod 13) 5 mod 7. 3) Use the Euclidean algorithm to find gcd(144,233).arrow_forward3 10) Suppose B = 2 4 5) and C = (b 2 prove that no such matrix exists. (6 1) . Find a matrix A such that AB = C orarrow_forward
- i let V-H.) R aluv) = (v) where alu)=SU. V dx and { and (v) sv Show that the finite element solution Un Unique Prove that U-Un ll≤ch llull A²=f and U= Ju =0 on on a with bili near from a (u,v) = SAU. Av dr 32 Prove that aluv) is countinous and V-expitic ii Prove that 2 Mete ||(U-U|| ²== ||||²+|| || ² where -Auf in U=0 on 2arrow_forwardConcdsider the following problem in R² ди -MAU+B+P+4= f inv ax U= 0 of 2 Bi-1, 2 are so prove. that al) is continous and, V-elliptic ⑥Provethat 14-Ull, s chllull zudx Where lull" = a(u,u) = £14. Ju 2 dx+ u.uds an let U= x(1-x)y (1-y) is gol. to -Au=f Compute || Ull Li and lull in are Ju, Duarrow_forwardMake Varitional for Malation for Problem and prove al.,.) is continous and, V-elliptic 224 2x² - -40² 4+24=1 ayz Xe=oonT 1 - €4 +x4 +4 = f XE I = (0,2), 4(a)=(()=0 (iii) - Au+S4=f Xen yo U=0, XE INarrow_forward
- 4) Given: LMNP is a parallelogram, PRSM, LR 1 PM, and NS 1 PM Prove: PS MR Statement Reason P L S R N Marrow_forward5) Given: Quadrilateral MNPQ with Fill in the missing reasons to show MNPQ is a parallelogram. 1/4 and 2 = 3. M N 1 2 4 3 Reason P Statement 1. 1 ≈ 4 and 2 = <3 1. Given 2. NQ=NQ 2. 3. AMNQ = APQN 3. 4. MN QP and NP = MQ 4. 5. MNPQ is a parallelogram 5.arrow_forward3) Given: EFGH is a parallelogram and ZH is a right angle. Prove: EFGH is a rectangle. E F G Harrow_forward
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