Question

Given: AB = CD

Prove: AC = BD
What reason can be used to justify statement 3 in the proof above?
the addition property the subtraction property the division property the substitution property

Answer 1

To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.

In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.

Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.