(Property of Equality) Use the following information to answer the question. Given: A, B, C, and D are collinear points.

Question

Use the following information to answer the question.

Given: A, B, C, and D are collinear points.

B is between A and C.

C is between B and D.

B and C are both between A and D.

AB=CD

Prove: AC=BD

Statements Reasons

1 AB=CD Given

2 BC=BC Reflexive Property of Equality

3 AB+BC=BC+CD ?

4 B is between A and C. Given

5 AB+BC=AC Definition of between

6 AC=BC+CD Substitution Property of Equality

7 C is between B and D. Given

8 BC+CD=BD Definition of between

9 AC=BD Substitution Property of Equality

What is the reason for Statement 3?

a) Subtraction Property of Equality

b) Reflexive Property of Equality

c) Transitive Property of Equality

d) Addition Property of Equality

e) Multiplication Property of Equality

f) Division Property of Equality

g) Substitution Property of Equality

I think the answer is d)Addition Property of Equality

Answer 1

You are adding the same thing to both sides so that the equation remains equal. Therefore you are correct, it is d. Good instincts. All the other [Four-Function Operation] Properties of Equality are pretty similar in this way. Do the operation with the same number on both sides and the equation remains true.