Given:
In triangle XYZ, J, K and L are midpoints of the sides.
JK = 38, XZ = 96, YX = 56.
To find:
KL, YZ and LZ.
Solution:
We have, J, K and L are midpoints of the sides of triangle XYZ.
JK = 38, XZ = 96, YX = 56.
Midsegment theorem: If a line segment between the midpoints of two sides of the triangle, then the length of the segment is half of the third side.
Using midsegment theorem, we get
[tex]KL=\dfrac{1}{2}YX[/tex]
[tex]KL=\dfrac{1}{2}(56)[/tex]
[tex]KL=28[/tex]
And,
[tex]JK=\dfrac{1}{2}YZ[/tex]
[tex]38=\dfrac{1}{2}YZ[/tex]
[tex]76=YZ[/tex]
L is the midpoint of the side YZ. So,
[tex]YL=LZ=\dfrac{1}{2}YZ[/tex]
[tex]YL=LZ=\dfrac{1}{2}(76)[/tex]
[tex]YL=LZ=38[/tex]
Therefore, the measures of KL, YZ and LZ are 28, 76 and 38 respectively.
