Question

challenge #1 using the segment addition postulate, part 1 a) select all statements that must be true. (select all that apply.) wz+zx+xy = wy wz = zx wz+zx = wy wz+zy = wy wx+xy = wy part 2 b.) wx = 2n + 5, xy = 3n - 1, and wy = 19 find the length of xy.

Explanation:

Step1: Recall segment - addition postulate

The segment - addition postulate states that if we have three collinear points \(A\), \(B\), and \(C\) where \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\).
For points \(W\), \(Z\), \(X\), \(Y\) on a line:

• For the statement \(WZ + ZX+XY = WY\), since \(WZ+ZX = WX\) and \(WX + XY=WY\), this statement is true.
• There is no information to suggest \(WZ = ZX\), so this statement is not necessarily true.
• \(WZ+ZX=WX

eq WY\), so \(WZ + ZX=WY\) is false.

• Since \(ZY=ZX + XY\), then \(WZ+ZY=WZ + ZX+XY=WY\), this statement is true.
• Since \(WX+XY = WY\) by the segment - addition postulate, this statement is true.

Step2: Solve for \(n\) in Part 2

We know that \(WX+XY = WY\) by the segment - addition postulate.
Given \(WX = 2n + 5\), \(XY=3n - 1\), and \(WY = 19\).
Substitute into the equation: \((2n + 5)+(3n - 1)=19\).
Combine like - terms: \(2n+3n+5 - 1=19\), which simplifies to \(5n+4 = 19\).
Subtract 4 from both sides: \(5n=19 - 4=15\).
Divide both sides by 5: \(n=\frac{15}{5}=3\).

Step3: Find the length of \(XY\)

Substitute \(n = 3\) into the expression for \(XY\).
\(XY=3n - 1\), so \(XY=3\times3 - 1=9 - 1 = 8\).

Answer:

Part 1:

• WZ+ZX+XY = WY
• WZ+ZY = WY
• WX+XY = WY

Part 2: 8