Question

In a proof it is known for line segments that AB + BC = BC + CD Which of the following would allows us to conclude AB and overline CD have the same length ?

Answer 1

By applying the Subtraction Property of Equality to the equation AB + BC = BC + CD, we can deduce that line segments AB and CD are equal in length.

Step-by-step explanation:

To conclude that line segments AB and CD have the same length, you must apply the concept of segment addition and the properties of equality. The equation provided states that AB + BC equals BC + CD. By the Subtraction Property of Equality, if you subtract BC from both sides of the equation, you're left with AB = CD, meaning line segments AB and CD are equal in length. This property is also applicable to general numerical operations where A + B is the same as B + A, indicating the commutative property of addition.