Question

Which statements must be true?
Select each correct answer.
• XY = 2CA
- AB || XZ
o CB = BA
CA= YZ
CB || XY

Answer 1

Step-by-step explanation:

By mid-point formula:

$\overline {AB} ||\overline {XZ} \\ \\

CA = \frac{1}{2} YZ\\ \\

\overline {CB} ||\overline {XY} \\ are \: true$

Answer 2

    Given triangle XYZ will follow the midsegment theorem.

By this theorem, statements given in options (2), (4) and (5) are correct.

   From the picture attached,

• CX = CZ
• BY = BZ
• AX = AY

ΔXYZ will follow the midsegment theorem which states,

"Segment connecting the midpoints of two sides of a triangle is parallel and half of the third side of the triangle"

• BC = $\frac{1}{2}XY$  

• AC = $\frac{1}{2}YZ$
• AB = $\frac{1}{2}XZ$
• CB ║XY
• AC ║YZ
• AB ║XZ

 Therefore, Options (2), (4) and (5) are the correct options.

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