Question

Suppose you were to use the following plan to write a proof. What would be your reason for step 3?

Given: Segment AB contains points A, X, Y, and B. X is the midpoint of segment AY, and Y is the midpoint of segment XB.
Prove: Segment AX is congruent to segment YB.
Plan: Use the definition of midpoint and the Transitive Property of Congruence.

1. X is the mipoint of AY Y is the midpoint of XB. (Reason: Given)
2. AX is congruent to XY, and XY is congruent to YB. (Reason: Definition of midpoint)
3. AX is congruent to YB ( Reason: ?? )

Answer 1

Do you remember the transitive property of equality?

Answer 2

Yeah

Answer 3

For all real numbers a, b, and c: If a = b and b = c, then ?

Answer 4

then a=c

Answer 5

Good! Now look at the proof again and see where it fits in.