Question

May you please give me the answers?

Answer 1

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

$KL=\dfrac{1}{2}YX$

$KL=\dfrac{1}{2}(56)$

$KL=28$

And,

$JK=\dfrac{1}{2}YZ$

$38=\dfrac{1}{2}YZ$

$76=YZ$

L is the midpoint of the side YZ. So,

$YL=LZ=\dfrac{1}{2}YZ$

$YL=LZ=\dfrac{1}{2}(76)$

$YL=LZ=38$

Therefore, the measures of KL, YZ and LZ are 28, 76 and 38 respectively.