Please write a paragraph proof for this statement. 30: 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

Question Help Find the midpoint of the line segment joining points A and B. A(8,-7); B

To prove that line XY is congruent to line ZW, we need to show that they have the same length. Given that Y is the midpoint of segment XZ, we can conclude that XY and XZ have equal lengths. This is because the midpoint of a line segment divides it into two equal halves. Now, we are also given that Z is the midpoint of segment YW. This implies that ZW and YW have equal lengths. So, we have XY = XZ and ZW = YW. Thus, by the Transitive Property of Equality, XY = ZW. Therefore, line XY is congruent to line ZW.

To prove that segment or line XY is congruent to segment or line ZW, we can use the definition of midpoint. We are given that point Y is the midpoint of segment XZ, which means that Y divides XZ into two congruent segments. Similarly, we are given that Z is the midpoint of segment YW, so Z divides YW into two congruent segments. Now, let's consider triangle XYZ and triangle ZWY.

In triangle XYZ, we know that XY is a segment connecting points X and Y, and XZ is a segment connecting points X and Z. Since Y is the midpoint of segment XZ, we can conclude that segments XY and YZ are congruent.

Now, in triangle ZWY, we know that ZW is a segment connecting points Z and W, and YW is a segment connecting points Y and W. Since Z is the midpoint of segment YW, we can conclude that segments ZW and WY are congruent.

Now, by the transitive property of congruence, if segment XY is congruent to segment YZ, and segment ZW is congruent to segment WY, then segment XY is congruent to segment or line ZW. Therefore, we have successfully proven that segment or line XY is congruent to segment or line ZW.