Construct an equilateral triangle and its three altitudes. What does intuition tell you about the three medians, the three angle bisectors, and the three perpendicular bisectors of the sides of that triangle?
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Elementary Geometry for College St...
6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698
BuyFindarrow_forward
Elementary Geometry for College St...
6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698
Solutions
Chapter
Section
Chapter 3.4, Problem 38E
Textbook Problem
Construct an equilateral triangle and its three altitudes. What does intuition tell you about the three medians, the three angle bisectors, and the three perpendicular bisectors of the sides of that triangle?
| Construct an equilateral triangle and its three altitudes. What does intuition tell you about the three medians, the three angle bisectors, and the three perpendicular bisectors of the sides of that triangle? |
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Expert Solution
Chapter 3 Solutions
Elementary Geometry for College Students
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addCh. 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 - In Exercises 39 to 40, complete each proof. Given:...Ch. 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 - 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 - In Exercise 13and 14, complete each proof. Given:...Ch. 3.2 - In Exercise 13and 14, complete each proof. Given:...Ch. 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 - In Exercise 30 to 32, draw the triangle that is to...Ch. 3.2 - In Exercises 30 to 32, draw the triangles that are...Ch. 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 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 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 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 - 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 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - Given that ABC is isosceles with ABAC, give the...Ch. 3.3 - Is it possible for a triangle to be: a an acute...Ch. 3.3 - A surveyor knows that a lot has the shape of an...Ch. 3.3 - In concave quadrilateral ABCD, the angle at A...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 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 - In Exercises 35 and 36, complete each proof using...Ch. 3.3 - In Exercises 37 to 39, complete each proof....Ch. 3.3 - In Exercises 37 to 39, complete each proof. Given:...Ch. 3.3 - In Exercises 37 to 39, complete each proof. Given:...Ch. 3.3 - In isosceles triangle BAT, ABAT.Also, BRBTAR, if...Ch. 3.3 - In BAT, BRBTAR, and mRBT=20. Find: a mT b mARB c...Ch. 3.3 - In PMN, PMPN, MB bisects PMN and NA bisects PNM....Ch. 3.3 - ABC lies in the structural support system of the...Ch. 3.3 - In Exercises 44 to 44, explain why each statement...Ch. 3.3 - In Exercises 46 to 48, explain why each statement...Ch. 3.3 - In Exercises 44 to 46, explain why each statement...Ch. 3.3 - Given: In the figure, XZYZ and Z is the midpoint...Ch. 3.3 - Given : In the figure, a=e=66. Also, YZZW. If...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to 12, use, the angles provided to...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to 12, use, the angles provided to...Ch. 3.4 - In Exercises 13 and 14. use the angles and lengths...Ch. 3.4 - In Exercises 13 and 14. use the angles and lengths...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - Describe how you would construct an angle...Ch. 3.4 - Describe how you would construct an angle...Ch. 3.4 - Construct the complement of the acute angle Q...Ch. 3.4 - Construct the supplement of the obtuse angle T...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercise 27 and 28, use the given angle R and...Ch. 3.4 - In Exercise 27 and 28, use the given angle R and...Ch. 3.4 - Complete the justification of the construction of...Ch. 3.4 - Given: AB with ACBCADBD by construction Prove:...Ch. 3.4 - To construct a regular hexagon, what measure would...Ch. 3.4 - To construct a regular octagon, what measure would...Ch. 3.4 - To construct a regular dodecagon 12 sides, what...Ch. 3.4 - Draw an acute triangle and construct the three...Ch. 3.4 - Draw an obtuse triangle and construct the three...Ch. 3.4 - Draw a right triangle and construct the angle...Ch. 3.4 - Draw an obtuse triangle and construct the three...Ch. 3.4 - Construct an equilateral triangle and its three...Ch. 3.4 - A carpenter has placed a square over an angle in...Ch. 3.4 - In right triangle ABC, mC=90. Also, BC=a, CA=b,...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 - 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 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 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 - A triangle is both isosceles and acute. If one...Ch. 3.5 - One of the angles of an isosceles triangle...Ch. 3.5 - NASA in Huntsville, Alabama at point H, has called...Ch. 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 - In Exercises 25 and 26, complete each proof shown...Ch. 3.5 - In Exercises 27 and 28, construct proofs. Given:...Ch. 3.5 - In Exercises 27 and 28, construct proofs. Given:...Ch. 3.5 - For ABC and DEF not shown, suppose that ACDF, ABDE...Ch. 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 - 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 - 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 - Given: OAOB OC is the median to AB Prove: OCABCh. 3.CR - Given: ABDE ABDE ACDF Prove: BCFECh. 3.CR - Given: B is the midpoint of AC BDAC Prove: ADC is...Ch. 3.CR - Given: JMGM and GKJK GHHJ Prove: GMJKCh. 3.CR - Given: TNTRTONPTSPRTOTS Prove: NRCh. 3.CR - Given: YZ is the base of an isosceles triangle;...Ch. 3.CR - Given: ABDCABDC C is the midpoint of BE Prove:...Ch. 3.CR - Given: BADCDA ABCD Prove: AEDE HINT: Prove BADCDA...Ch. 3.CR - Given: BE is the altitude to AC AD is the altitude...Ch. 3.CR - Given: ABCDBADCDA Prove: AED is isosceles HINT:...Ch. 3.CR - Given: AC bisects BAD Prove: ADCDCh. 3.CR - In PQR not shown, mP=67 and mQ=23. a Name the...Ch. 3.CR - In ABC not shown, mA=40 and mB=65. List the sides...Ch. 3.CR - In PQR not shown, PQ=1.5, PR=2, and QR=2.5. List...Ch. 3.CR - Name the longest line segment shown in...Ch. 3.CR - Which of the following can be the lengths of the...Ch. 3.CR - Two sides of a triangle have lengths 15 and 20....Ch. 3.CR - Given:DBACADDCmC=70Find:mADBCh. 3.CR - Given: ABBCDACBCDmB=50 Find: mADCCh. 3.CR - Given: ABC is isosceles with base AB...Ch. 3.CR - Given: ABC with perimeter 40 AB=10BC=x+6AC=2x3...Ch. 3.CR - Given: ABC is isosceles with base AB...Ch. 3.CR - Given: AC and BC are the legs of isosceles ABC...Ch. 3.CR - Construct an angle that measures 75.Ch. 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 - State the reason SSS, SAS, ASA, AAS, or HL why The...Ch. 3.CT - Write the statement that is represented by the...Ch. 3.CT - With congruent parts marked, are the two triangles...Ch. 3.CT - With ABDCBE and A-D-E-C, does it necessarily...Ch. 3.CT - In ABC, mC=90 Find : a c if a=8 and b=6_ b b if...Ch. 3.CT - CM is the median for ABC from vertex C to side AB....Ch. 3.CT - In TUV, TVUV. Exercises 9, 10 a If mT=71, find mV....Ch. 3.CT - In TUV, TU. a If VT=7.6inches and TU=4.3inches,...Ch. 3.CT - Show all arcs in the following construction. a...Ch. 3.CT - Show all arcs in the following construction....Ch. 3.CT - In ABC, mC=46 and mB=93. a Name the shortest side...Ch. 3.CT - In TUV not shown, TUTVVU. Write a three-part...Ch. 3.CT - In the figure, A is the right angle,...Ch. 3.CT - Given ABC, draw the triangle that results when ABC...Ch. 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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