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Math Geometry Elementary Geometry for College Students

To construct: The angle of 90 ° and 45 ° .

To construct: The angle of 90 ° and 45 ° .

Solution Summary: The author explains the angle of measure 90° and 45°.

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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Concept explainers

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 3.4, Problem 15E

To determine

To construct:

The angle of 90° and 45°.

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Chapter 3.4, Problem 14E

Chapter 3.4, Problem 16E

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. 39E 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 - Prob. 9E 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. 13E Ch. 3.2 - Prob. 14E 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 - Prob. 30E Ch. 3.2 - Prob. 31E 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 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - Prob. 10E 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 - Prob. 14E 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 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Is it possible for a triangle to be: a an acute...Ch. 3.3 - Prob. 21E Ch. 3.3 - In concave quadrilateral ABCD, the angle at A...Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E 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 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - In isosceles triangle BAT, ABAT.Also, BRBTAR, if...Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Given: In the figure, XZYZ and Z is the midpoint...Ch. 3.3 - Prob. 48E Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Prob. 7E Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - In Exercises 13 and 14. use the angles and lengths...Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Prob. 17E Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - Prob. 24E Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - Prob. 26E Ch. 3.4 - In Exercise 27 and 28, use the given angle R and...Ch. 3.4 - Prob. 28E Ch. 3.4 - Complete the justification of the construction of...Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E 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 - Prob. 38E Ch. 3.4 - A carpenter has placed a square over an angle in...Ch. 3.4 - Prob. 40E 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 - Prob. 15E Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - Prob. 17E 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 - Prob. 21E Ch. 3.5 - One of the angles of an isosceles triangle...Ch. 3.5 - Prob. 23E 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 - Prob. 26E 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 - Prob. 29E 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 - Prob. 33E 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: AEBDEC Ch. 3.CR - Given: ABEFACDF12 Prove: BE Ch. 3.CR - Given: AD bisects BC ABBCDCBC Prove: AEDE Ch. 3.CR - Prob. 4CR Ch. 3.CR - Prob. 5CR Ch. 3.CR - Given: B is the midpoint of AC BDAC Prove: ADC is...Ch. 3.CR - Prob. 7CR Ch. 3.CR - Prob. 8CR Ch. 3.CR - Given: YZ is the base of an isosceles triangle;...Ch. 3.CR - Prob. 10CR Ch. 3.CR - Prob. 11CR Ch. 3.CR - Prob. 12CR Ch. 3.CR - Prob. 13CR Ch. 3.CR - Given: AC bisects BAD Prove: ADCD Ch. 3.CR - Prob. 15CR Ch. 3.CR - Prob. 16CR Ch. 3.CR - Prob. 17CR Ch. 3.CR - Name the longest line segment shown in...Ch. 3.CR - Prob. 19CR Ch. 3.CR - Two sides of a triangle have lengths 15 and 20....Ch. 3.CR - Prob. 21CR Ch. 3.CR - Prob. 22CR Ch. 3.CR - Prob. 23CR Ch. 3.CR - Prob. 24CR Ch. 3.CR - Given: ABC is isosceles with base AB...Ch. 3.CR - Prob. 26CR Ch. 3.CR - Prob. 27CR 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 - Prob. 3CT Ch. 3.CT - Prob. 4CT Ch. 3.CT - With congruent parts marked, are the two triangles...Ch. 3.CT - Prob. 6CT Ch. 3.CT - Prob. 7CT Ch. 3.CT - CM is the median for ABC from vertex C to side AB....Ch. 3.CT - Prob. 9CT Ch. 3.CT - Prob. 10CT Ch. 3.CT - Prob. 11CT Ch. 3.CT - Show all arcs in the following construction....Ch. 3.CT - Prob. 13CT Ch. 3.CT - Prob. 14CT Ch. 3.CT - Prob. 15CT Ch. 3.CT - Prob. 16CT 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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