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

subtraction property of equality

Answer 2

Answer:

The correct option is D.

Step-by-step 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.