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=(1)/(2)YX`

`KL=(1)/(2)(56)`

`KL=28`

And,

`JK=(1)/(2)YZ`

`38=(1)/(2)YZ`

`76=YZ`

L is the midpoint of the side YZ. So,

`YL=LZ=(1)/(2)YZ`

`YL=LZ=(1)/(2)(76)`

`YL=LZ=38`

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