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

Question

asked Jul 1, 2019 231k views

1 Answer

Duduklein · Answer 1 · 2019-07-07T05:44:56+0000

Answer:

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.