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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 2.2, Problem 11E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
69 views

Which of the following statements would you prove by the indirect method?

a) In triangle A B C , if m ∠ A > m ∠ B , then A C ≠ B C .

b) If alternate exterior ∠ 1 ≅ alternate exterior ∠ 8 , then l is not parallel to m .

c) If ( x + 2 ) ⋅ ( x − 3 ) = 0 , then x = − 2   or   x = 3 .

d) If two sides of a triangle are congruent, the two angles opposite these sides are also congruent.

e) The perpendicular bisector of a line segment is unique.

To determine

(a)

Whether the statement, “In triangle ABC, if m∠A>m∠B, then AC≠BC” can be proved by the indirect method.

Explanation

Approach:

(1) To prove the statement P→Q by the indirect method, the following steps are used:

1. Suppose that ∼Q is true.

2. Reason from the supposition until you reach a contradiction.

3. Note that the supposition claiming that ∼Q is true must be false and that Q must therefore be true.

Step 3 completes the proof.

(2) The sides opposite to equal angles in a triangle are also equal.

Calculation:

Consider the given statement, “In triangle ABC, if m∠A>m∠B, then AC≠BC”

To determine

(b)

Whether the statement, “If alternate exterior ∠1≅ alternate exterior ∠8, then 𝓁 is not parallel to m” can be proved by the indirect method.

To determine

(c)

Whether the statement, “If (x+2)⋅(x−3)=0, then x=−2 or x=3” can be proved by the indirect method.

To determine

(d)

Whether the statement, “If two sides of a triangle are congruent, the two angles opposite these sides are also congruent.” can be proved by the indirect method.

To determine

(e)

Whether the statement, “The perpendicular bisector of a line segment is unique” can be proved by the indirect method”.

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Chapter 2.2,
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Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E
Sect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ESect-2.4 P-45ESect-2.4 P-46ESect-2.4 P-47ESect-2.4 P-48ESect-2.4 P-49ESect-2.4 P-50ESect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-24ESect-2.6 P-25ESect-2.6 P-26ESect-2.6 P-27ESect-2.6 P-28ESect-2.6 P-29ESect-2.6 P-30ESect-2.6 P-31ESect-2.6 P-32ESect-2.6 P-33ESect-2.6 P-34ESect-2.6 P-35ESect-2.6 P-36ESect-2.CR P-1CRSect-2.CR P-2CRSect-2.CR P-3CRSect-2.CR P-4CRSect-2.CR P-5CRSect-2.CR P-6CRSect-2.CR P-7CRSect-2.CR P-8CRSect-2.CR P-9CRSect-2.CR P-10CRSect-2.CR P-11CRSect-2.CR P-12CRSect-2.CR P-13CRSect-2.CR P-14CRSect-2.CR P-15CRSect-2.CR P-16CRSect-2.CR P-17CRSect-2.CR P-18CRSect-2.CR P-19CRSect-2.CR P-20CRSect-2.CR P-21CRSect-2.CR P-22CRSect-2.CR P-23CRSect-2.CR P-24CRSect-2.CR P-25CRSect-2.CR P-26CRSect-2.CR P-27CRSect-2.CR P-28CRSect-2.CR P-29CRSect-2.CR P-30CRSect-2.CR P-31CRSect-2.CR P-32CRSect-2.CR P-33CRSect-2.CR P-34CRSect-2.CR P-35CRSect-2.CR P-36CRSect-2.CR P-37CRSect-2.CR P-38CRSect-2.CR P-39CRSect-2.CR P-40CRSect-2.CR P-41CRSect-2.CR P-42CRSect-2.CR P-43CRSect-2.CR P-44CRSect-2.CR P-45CRSect-2.CR P-46CRSect-2.CR P-47CRSect-2.CT P-1CTSect-2.CT P-2CTSect-2.CT P-3CTSect-2.CT P-4CTSect-2.CT P-5CTSect-2.CT P-6CTSect-2.CT P-7CTSect-2.CT P-8CTSect-2.CT P-9CTSect-2.CT P-10CTSect-2.CT P-11CTSect-2.CT P-12CTSect-2.CT P-13CTSect-2.CT P-14CTSect-2.CT P-15CTSect-2.CT P-16CTSect-2.CT P-17CTSect-2.CT P-18CTSect-2.CT P-19CT

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