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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.5, Problem 38E
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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
Problem 35E
Problem 36E
Problem 37E
Problem 38E
BuyFindarrow_forward

Elementary Geometry for College St...

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

Write a proof for: “If a = b and c = d , then a − c = b − d .”

(HINT: Use Exercise 39 as a guide)

39. Provide reasons for this proof. “If a = b and c = d , then a + c = b + d .”

PROOF
Statements Reasons
1. a = b 1. ?
2. a + c = b + c 2. ?
3. c = d 3. ?
4. a + c = b + d 4. ?

To determine

To find:

The proof for the given condition.

Explanation

Given:

a=b and c=d

Property used:

1. The Subtraction Property of Equality states that if a number is subtract from one side of an equation then the same number must be subtracted from the other side of equation to maintain the equality of the original equation.

2. According to Substitution Property of Equality, if A=B, then A can be substituted for B and B can be substituted for A in any equation.

Calculation:

The first statement of the proof should be the given part.

a=b

Therefore, the first statement for the proof is a=b and the reason for the first statement is given.

Use Subtraction Property of Equality and subtract c from both side of the equation.

a−c=b−c

Therefore, the second statement of the proof is a−c=b−c and the reason for second statement is Subtraction Property of Equality.

In the right side of the final equation, it is only d in place of c. In order to get this, consider the remaining part of the given.

c=d

Therefore, the third statement of the proof is c=d and the reason for the third statement is given.

To reach the final statement, use second statement.

a−c=b−c

Use Substitution Property of Equality and substitute d for c in the right side of equation as c=d

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