Question

What is the missing reason in the proof?

A.
segment addition
B.
Congruent Segments Theorem
C.
Transitive Property of Equality
D.
Subtraction Property of Equality

Answer 1

The correct option is D.

Explanation:

It is given that

`AB\cong CD`

Using definition of congruent segment.

`AB=CD` .... (1)

Using segment addition.

`AB=AE+EB`

`CD=CF+FD`

Using segment addition in equation (1).

`AE+EB=CF+FD` .... (2)

It is given that

`CF\cong EB`

Using definition of congruent segment.

`CF=EB` .... (3)

Using (2) and (3) we get

`AE+EB=EB+FD`

Using subtraction property of equality, subtract EB from both the sides.

`AE=FD`

Using definition of congruent segment.

`AE\cong FD`

The missing reason is "Subtraction Property of Equality". Hence option D is correct.