Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Chapter 3.CT, Problem 14CT
To determine
To write:
A three-part inequality that compares the measures of the three
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HOMEWORK: 18, 19, 24, 27, 29
***Please refer to the HOMEWORK sheet from Thursday, 9/14, for
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****Please text or email me if you have any questions
18. Figure 5-35 is a map of downtown Royalton, showing
the Royalton River running through the downtown
area and the three islands (A, B, and C) connected to
each other and both banks by eight bridges. The Down-
town Athletic Club wants to design the route for a
marathon through the downtown area. Draw a graph
that models the layout of Royalton.
FIGURE 5-35
North Royalton
Royalton River
South Royption
19. A night watchman must walk the streets of the Green
Hills subdivision shown in Fig. 5-36. The night watch-
man needs to walk only once along each block. Draw a
graph that models this situation.
Solve this question and check if my answer provided is correct
Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.
Chapter 3 Solutions
Elementary Geometry for College Students
Ch. 3.1 - In Exercises 1 to 4, consider the congruent...Ch. 3.1 - In Exercises 1 to 4. consider the congruent...Ch. 3.1 - In Exercises 1 to 4. consider the congruent...Ch. 3.1 - In Exercises 1 to 4, consider the congruent...Ch. 3.1 - Consider ABC and ABD in the figure shown. By the...Ch. 3.1 - In a right triangle, the sides that form the right...Ch. 3.1 - In ABC, the midpoints of the sides are joined. a...Ch. 3.1 - a. Suppose that you wish to prove that RSTSRV....Ch. 3.1 - In Exercises 9 to 12, congruent parts are...Ch. 3.1 - In Exercises 9 to 12, congruent parts are...
Ch. 3.1 - In Exercises 9 to 12, congruent parts are...Ch. 3.1 - In Exercises 9 to 12, congruent parts are...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 19 and 20, the triangles to be proved...Ch. 3.1 - In Exercises 19 and 20, the triangles to be proved...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 25 and 26, complete each proof. Use...Ch. 3.1 - In Exercises 25 and 26, complete each proof. Use...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 33 to 36, the methods to be used are...Ch. 3.1 - In Exercises 33 to 36, the methods to be used are...Ch. 3.1 - In Exercises 33 to 36, the method to be used are...Ch. 3.1 - In Exercises 33 to 36, the method to be used are...Ch. 3.1 - In quadrilateral ABCD, AC and BD are perpendicular...Ch. 3.1 - In ABC and DEF, you know that AD, CF, and ABDE....Ch. 3.1 - Prob. 39ECh. 3.1 - In Exercises 39 to 40, complete each proof. Given:...Ch. 3.1 - Given: ABC; RS is the perpendicular bisector of...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - Prob. 9ECh. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Given: HJ bisects KHL HJKL See figure for exercise...Ch. 3.2 - Given: HJ bisects KHL HJKL In Exercise 15, you cam...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 27 to 29, prove the indicated...Ch. 3.2 - In Exercise 27 to 29, prove the indicated...Ch. 3.2 - In Exercise 27 to 29, prove the indicated...Ch. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - In Exercises 30 to 32, draw the triangles that are...Ch. 3.2 - Given: RW bisects SRU Prove: RSRU TRUVRS HINT:...Ch. 3.2 - Given: DBBC and CEDE Prove: ABAE BDCECD HINT:...Ch. 3.2 - In the roof truss shown, AB=8 and mHAF=37. Find: a...Ch. 3.2 - In the support system of the bridge shown, AC=6ft...Ch. 3.2 - As a car moves along the roadway in a mountain...Ch. 3.2 - Because of the construction along the road from A...Ch. 3.2 - Given: Regular pentagon ABCDE with diagonals BE...Ch. 3.2 - In the figure with regular pentagon ABCDE, do BE...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - Prob. 10ECh. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - Prob. 14ECh. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Is it possible for a triangle to be: a an acute...Ch. 3.3 - Prob. 21ECh. 3.3 - In concave quadrilateral ABCD, the angle at A...Ch. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Suppose that ABCDEF. Also, AX bisects CAB and DY...Ch. 3.3 - Suppose that ABCDEF. Also, AX is the median from A...Ch. 3.3 - In Exercises 35 and 36, complete each proof using...Ch. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - In isosceles triangle BAT, ABAT.Also, BRBTAR, if...Ch. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Given: In the figure, XZYZ and Z is the midpoint...Ch. 3.3 - Prob. 48ECh. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - In Exercises 13 and 14. use the angles and lengths...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - Prob. 24ECh. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - Prob. 26ECh. 3.4 - In Exercise 27 and 28, use the given angle R and...Ch. 3.4 - Prob. 28ECh. 3.4 - Complete the justification of the construction of...Ch. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Draw a right triangle and construct the angle...Ch. 3.4 - Draw an obtuse triangle and construct the three...Ch. 3.4 - Prob. 38ECh. 3.4 - A carpenter has placed a square over an angle in...Ch. 3.4 - Prob. 40ECh. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - Is it possible to draw a triangle whose angles...Ch. 3.5 - Is it possible to draw a triangle whose angles...Ch. 3.5 - Is it possible to draw a triangle whose sides...Ch. 3.5 - Is it possible to draw a triangle whose sides...Ch. 3.5 - Prob. 15ECh. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - Prob. 17ECh. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - Two of the sides of an isosceles triangle have...Ch. 3.5 - The sides of a right triangle have lengths of 6cm,...Ch. 3.5 - Prob. 21ECh. 3.5 - One of the angles of an isosceles triangle...Ch. 3.5 - Prob. 23ECh. 3.5 - A tornado has just struck a small Kansas community...Ch. 3.5 - In Exercises 25 and 26, complete each proof shown...Ch. 3.5 - Prob. 26ECh. 3.5 - In Exercises 27 and 28, construct proofs. Given:...Ch. 3.5 - In Exercises 27 and 28, construct proofs. Given:...Ch. 3.5 - Prob. 29ECh. 3.5 - In MNP not shown, point Q lies on NP so that MQ...Ch. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - Prob. 33ECh. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - Prove by the indirect method: Given: MPN is not...Ch. 3.5 - Prove by the indirect method: Given: Scalene XYZ...Ch. 3.5 - In Exercises 37 and 38, prove each theorem. The...Ch. 3.5 - In Exercises 37 and 38, prove each theorem. The...Ch. 3.CR - Given: AEBDEC AEDE Prove: AEBDECCh. 3.CR - Given: ABEFACDF12 Prove: BECh. 3.CR - Given: AD bisects BC ABBCDCBC Prove: AEDECh. 3.CR - Prob. 4CRCh. 3.CR - Prob. 5CRCh. 3.CR - Given: B is the midpoint of AC BDAC Prove: ADC is...Ch. 3.CR - Prob. 7CRCh. 3.CR - Prob. 8CRCh. 3.CR - Given: YZ is the base of an isosceles triangle;...Ch. 3.CR - Prob. 10CRCh. 3.CR - Prob. 11CRCh. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Given: AC bisects BAD Prove: ADCDCh. 3.CR - Prob. 15CRCh. 3.CR - Prob. 16CRCh. 3.CR - Prob. 17CRCh. 3.CR - Name the longest line segment shown in...Ch. 3.CR - Prob. 19CRCh. 3.CR - Two sides of a triangle have lengths 15 and 20....Ch. 3.CR - Prob. 21CRCh. 3.CR - Prob. 22CRCh. 3.CR - Prob. 23CRCh. 3.CR - Prob. 24CRCh. 3.CR - Given: ABC is isosceles with base AB...Ch. 3.CR - Prob. 26CRCh. 3.CR - Prob. 27CRCh. 3.CR - Construct a right triangle that has acute angle A...Ch. 3.CR - Construct a second isosceles triangle in which the...Ch. 3.CT - It is given that ABCDEF triangles not shown a If...Ch. 3.CT - Consider XYZ triangles not shown a Which side is...Ch. 3.CT - Prob. 3CTCh. 3.CT - Prob. 4CTCh. 3.CT - With congruent parts marked, are the two triangles...Ch. 3.CT - Prob. 6CTCh. 3.CT - Prob. 7CTCh. 3.CT - CM is the median for ABC from vertex C to side AB....Ch. 3.CT - Prob. 9CTCh. 3.CT - Prob. 10CTCh. 3.CT - Prob. 11CTCh. 3.CT - Show all arcs in the following construction....Ch. 3.CT - Prob. 13CTCh. 3.CT - Prob. 14CTCh. 3.CT - Prob. 15CTCh. 3.CT - Prob. 16CTCh. 3.CT - Complete all statements and reasons for the...Ch. 3.CT - Complete all missing statements and reasons in the...Ch. 3.CT - The perimeter of an isosceles triangle is 32cm. If...
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