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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
Publisher: Cengage,
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
Publisher: Cengage,
ISBN: 9781337614085
Chapter 3.1, Problem 40E
Textbook Problem
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Are quadrilaterals ABCD and EFGH congruent if:

a) A B ¯ E F ¯ , B F , B C ¯ F G ¯ and C G ?
b) A E , A B ¯ E F ¯ , B F , B C ¯ F G ¯ , an C G ?

Chapter 3.1, Problem 40E, Are quadrilaterals ABCD and EFGH congruent if: a ABEF, BF, BCFG and CG? b AE, ABEF, BF, BCFG, an CG?

Exercises 39, 40

To determine

a)

To proof:

The quadrilaterals ABCD and EFGH are congruent, if two sides and two angles of quadrilaterals are congruent to each other.

Explanation of Solution

Given:

The quadrilaterals ABCD and EFGH are shown in the figure below,

Figure (1)

From figure (1),

AB¯EF¯BFBC¯FG¯CG

Calculation:

Consider the quadrilaterals,

ABCD and EFGH

From the given data, the two sides and two angles of quadrilaterals are congruent to each other

To determine

b)

To proof:

The quadrilaterals ABCD and EFGH are congruent, if two sides and three angles of quadrilaterals are congruent to each other.

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Chapter 3 Solutions

Elementary Geometry For College Students, 7e
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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 - Are quadrilaterals ABCD and EFGH congruent if: a...Ch. 3.1 - Are quadrilaterals ABCD and EFGH congruent if: a...Ch. 3.1 - In Exercises 41 to 42, complete each proof. Given:...Ch. 3.1 - In Exercises 41 to 42, 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 Prove: KL PROOF...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. 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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. 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The...Ch. 3.5 - In Exercises 37 and 38, prove each theorem. The...Ch. 3.5 - The perimeter of a triangle cannot have a measure...Ch. 3.5 - In isosceles MNP, MNMP. With point Q on MN,...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 - 2. Consider XYZ triangles not shown a Which side...Ch. 3.CT - 3. State the reason SSS, SAS, ASA, AAS, or HL why...Ch. 3.CT - Write the statement that is represented by the...Ch. 3.CT - 5. 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