Chapter 5.3, Problem 7CE

To determine

To state a theorem from the given figure

Answer to Problem 7CE

Midpoint Theorem

Explanation of Solution

Given:

  $M,N,$ and $T$ are the midpoints of the sides of $\Delta XYZ$ .

  

Midpoint Theorem: if the line joining mid points of any triangle is parallel to the third side of that triangle then this line equal to the half of the third side of the triangle.

Now in $\Delta XYZ$ ,

Since $T$ and $N$ are the midpoints of $ZX$ and $ZY$ respectively. So, according to Midpoint Theorem,

  $TN$ is parallel to $XY$ and $TN=\frac{1}{2}XY$ .

Since $N$ and $M$ are the midpoints of $ZY$ and $YX$ respectively. So, according to Midpoint Theorem,

  $NM$ is parallel to $ZX$ and $NM=\frac{1}{2}ZX$ .

Since $M$ and $T$ are the midpoints of $YX$ and $XZ$ respectively. So, according to Midpoint Theorem,

  $MT$ is parallel to $YZ$ and $MT=\frac{1}{2}YZ$ .

Conclusion:

Therefore, Midpoint Theorem is used in the given question.