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Given that segment AB is congruent to XY and O is the midpoint of both AB and XY we can use their common midpoint to prove segment XO is congruent to AO. Because segment AB = XY (they are equal if they are congruent) and both segments share the same midpoint, this means that the midpoint divides both segments into equal halves, seeing as a midpoint is a halfway point. Since both segments are congruent to each other, the segments XO and AO resulting from the midpoint that split segments AB and XY in half are congruent to each other because since segments AB and XY are congruent to each other their half values are also congruent and their half values are the segments XO and AO resulting from the midpoint split. Therefore, this proves that segments XO and AO are congruent.

Sagot :

dashataran

Answer:

Yes you're correct and I used similar concept in your previous question.

Step-by-step explanation:

Here's even a simpler way to understand this problem or solve the proof:

Given:

         [tex]\bullet\ \text{$\overline{AB}\cong\overline{XY}$ or AB = XY}[/tex]

         [tex]\bullet\ \text{O is the midpoint of $\overline{AB}$ and $\overline{XY}.$}[/tex]

Assumption:

         [tex]\text{Let's assume that $\overline{AB}=\overline{XY}=10$ units.}[/tex]

To prove:

  • [tex]\overline{AO}\cong\overline{XO}\text{$ or AO = XO}[/tex]

Proof:

    1.  Assume lengths:

        [tex]\text{Assume $\overline{XY}=10$ units and $\overline{AB}=10$ units}[/tex]

    2.  Midpoint Definition:

        [tex]\text{Since O is the midpoint of $\overline{AB}, $ the segment $\overline{AB}$ is divided into two}[/tex]

       [tex]\text{equal parts:$}\\[/tex]

                            [tex]\overline{AO}=\overline{BO}=\dfrac{10}{2}=5\text{$ units}[/tex]

        [tex]\text{$Similarly, since O is the midpoint of $\overline{XY}, $ the segment $\overline{XY}$ is divided }[/tex]

        [tex]\text{$into two equal parts:}[/tex]

                           [tex]\overline{XO}=\overline{YO}=\dfrac{10}{2}=5\text{$ units}[/tex]

   3.  Conclusion:

        From the above calculations, we see that:

                           [tex]\overline{AO}=\overline{XO}=5\text{$ units}[/tex]

        Thus, we have proved that:

                           [tex]\overline{AO}\cong\overline{XO}[/tex]

So, essentially, when you divide two congruent line segments into equal parts, all the resulting segments are equal to each other.

This solution was just for your understanding, I recommend you not to write this in your original assignment.

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