Question

look at the diagram and evaluate. which of the statements below is false?
answer
vw = wx
ux > uw
w is the midpoint of vx
vw > uv

Explanation:

Step1: Calculate the lengths

• \(VW = 16 - 13=3\)
• \(WX = 19 - 16 = 3\)
• \(UX=19 - 3 = 16\)
• \(UW=16 - 3=13\)
• \(UV = 13 - 3=10\)

Step2: Check each statement

• For \(VW = WX\):

Since \(VW = 3\) and \(WX = 3\), \(VW = WX\) is True.

• For \(UX>UW\):

Since \(UX = 16\) and \(UW = 13\), \(16>13\), so \(UX>UW\) is True.

• For \(W\) is the mid - point of \(\overline{VX}\):

\(VX=19 - 13 = 6\), and \(VW = 3\), \(WX = 3\), so \(W\) is the mid - point of \(\overline{VX}\), this statement is True.

• For \(VW>UV\):

Since \(VW = 3\) and \(UV = 10\), \(3<10\), so \(VW>UV\) is False.

Answer:

\(VW>UV\)