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

A) Reflexive Property of Congruence
B) Transtive Property of Congruence
C) Reflexive Property of Equality
D) Transitive Property of Equality

Answer 2

Look at statement 2:

\(\overline{AX} \cong \overline{XY}\) and \(\overline{XY} \cong \overline{YB}\)

This is similar to

If a = b, and b = c, then a = c.

What property of equality is this?

Also, your proof states that the plan is to use the definition of midpoint and the transitive property of congruent. The definition of midpoint was the reason for statement 2, so the definition of midpoint was already used. Now you need a reason for statement 3.