Question

which statement is true by the segment addition postulate?
a) wy = yz
b) wx + yz = wz
c) xy + wx = wz
d) zy + yx = zx

Explanation:

The Segment Addition Postulate states that if three points \( W \), \( X \), \( Y \), \( Z \) are collinear (in a straight line) with \( X \) between \( W \) and \( Y \), and \( Y \) between \( X \) and \( Z \), then the sum of the lengths of the smaller segments equals the length of the larger segment.

Step 1: Analyze Option A

\( WY = YZ \): From the diagram, \( WY \) is a longer segment than \( YZ \), so this is false.

Step 2: Analyze Option B

\( WX + YZ = WZ \): The Segment Addition Postulate for \( WZ \) should be \( WX + XY + YZ = WZ \), not \( WX + YZ \), so this is false.

Step 3: Analyze Option C

\( XY + WX = WZ \): The correct addition for \( WZ \) would involve \( XY \) and \( YZ \) as well, so \( WX + XY + YZ = WZ \), not \( XY + WX \), so this is false.

Step 4: Analyze Option D

\( ZY + YX = ZX \): By the Segment Addition Postulate, if \( Y \) is between \( Z \) and \( X \), then \( ZY + YX = ZX \). Looking at the diagram, \( Y \) is between \( Z \) and \( X \) (since the order is \( W - X - Y - Z \)? Wait, no, the diagram is \( W - X - Y - Z \) from left to right? Wait, no, the points are \( W \), \( X \), \( Y \), \( Z \) in order. Wait, actually, if we consider \( Z \), \( Y \), \( X \), \( W \) reversed, but the Segment Addition Postulate: if \( Y \) is between \( Z \) and \( X \), then \( ZY + YX = ZX \). Yes, this follows the postulate.

Answer:

D. \( ZY + YX = ZX \)