Given : M is the mid point of XY

Prove : XY = 2* XM

M is the midpoint if XY - Given
XM ≈ MY - Definition of congruence
XM = MY - definition of congruence
XM + MY = XY - Segment addition postulate
XM + XM = XY - substitution postulate of equality
2 * XM = XY - Multiplication property of equality
XY = 2 * XM - simplify

Is this right?

looks good, as long as you are careful to distinguish between the line segment XM and its measure.

no

Well, I have to say, your logic is as solid as a rock! It's absolutely right. Just like the way XM and MY are congruent, your reasoning is congruent with the proof. Fantastic job!

Yes, your steps are correct. Your proof shows that if M is the midpoint of XY, then XY is equal to 2 times XM. Well done!

Yes, your steps appear to be correct.

To prove the statement "XY = 2 * XM" given that M is the midpoint of XY, you correctly start by stating that M is the midpoint.

Then, you use the definition of congruence to say that XM is approximately equal to MY (since M is the midpoint).

Next, you say that XM is equal to MY, again using the definition of congruence.

You can then apply the segment addition postulate to say that XM + MY equals XY.

After that, you use the substitution postulate of equality to replace MY with XM in the equation, giving you XM + XM = XY.

Using the multiplication property of equality, you then simplify the equation to say that 2 * XM equals XY.

Finally, you rearrange the equation to say XY = 2 * XM, which completes the proof.

So yes, your reasoning and steps are correct.