Please write a paragraph proof for this statement. Point Y is the midpoint of segment XZ. Z is the midpoint of segment YW. PRove that segment or line XY is congruent to segment or line ZW.

since point Y is the midpoint of XZ, XY = YZ. since point Z is the midpoint of YW, YZ = ZW. therefore, XY = YZ = ZW.

so there,, i'm not good at writing a paragraph~ :P

I have a question :

find the midpoint of a segment DE with point D at (-8, 2) and point E, at (4, -2)
-(-2,0)
-(-6, 2)
-(-6, -2)
-(-3, -1)
i need help !! QUICK

Sure, I'd be happy to help with that! But first, let me ask you a question: Why did the line fall down? Because it was parallel to the ground! Now, let's dive into the proof!

Given: Y is the midpoint of XZ, and Z is the midpoint of YW.

To prove: XY ≅ ZW

Proof:

1. Y is the midpoint of XZ Given
2. Z is the midpoint of YW Given
3. XY ≅ XZ Definition of midpoint
4. ZW ≅ YW Definition of midpoint
5. XZ ≅ YW Transitive Property of Congruence
6. XY ≅ ZW Substitution Property of Equality

And there you have it! XY is congruent to ZW because of the given information and our lovely steps of the proof. Just remember, it's always important to add a touch of humor when proving a point!

We want to prove that segment XY is congruent to segment ZW.

1. Given - Point Y is the midpoint of segment XZ, and point Z is the midpoint of segment YW.
2. By the definition of midpoint, we know that XY and XZ have equal lengths, and ZW and YW have equal lengths.
3. By the Transitive Property of Equality, if XY and XZ have equal lengths, and ZW and YW have equal lengths, then XY and ZW must have equal lengths.
4. Therefore, segment XY is congruent to segment ZW. Q.E.D.

To prove that segment or line XY is congruent to segment or line ZW, we will use the definition of midpoint and the Transitive Property of Equality.

1. Given: Point Y is the midpoint of segment XZ, and Z is the midpoint of segment YW.
2. By the definition of midpoint, we know that segment XY is bisected at point Y, meaning that Y divides the segment into two congruent parts, XY and YZ.
3. Similarly, by the definition of midpoint, we know that segment ZW is bisected at point Z, meaning that Z divides the segment into two congruent parts, ZY and YW.
4. Since Y is the midpoint of segment XY and Z is the midpoint of segment ZW, we can say that XY is congruent to YZ and ZY is congruent to YW.
5. Applying the Transitive Property of Equality, if XY is congruent to YZ and YZ is congruent to ZY, then we can conclude that XY is congruent to ZY.
6. Again, applying the Transitive Property of Equality, if XY is congruent to ZY and ZY is congruent to YW, then it follows that XY is congruent to YW.
7. Hence, segment XY is congruent to segment ZW (or line XY is congruent to line ZW), as desired.

Therefore, we have proven that segment or line XY is congruent to segment or line ZW using the definitions of midpoint and the Transitive Property of Equality.