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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

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

ac=bc

Therefore, the second statement of the proof is ac=bc 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.

ac=bc

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

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