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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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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 missing reasons for the algebraic proof.

Explanation

Given:

The given table is shown below.

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

Property used:

1. The Addition Property of Equality states that if same number is added to both sides of the equation then the sides of the equation remains equal.

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 is given below.

a=b

The first statement is same as the given equation. So, the reason for the first statement is given.

Now, go from the first statement to the second statement.

a=b

Use Addition Property of Equality and add c in both side of the equation.

a+c=b+c

Therefore, the reason for second statement is Addition Property of Equality.

Consider the third statement of the proof.

c=d

The third statement is a part of the given information. So, the reason for the third statement is given.

To reach the final statement, use second statement

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