Question

Which statements must be true?

Select each correct answer.


UW=VW

UW=12KL

JK=2VW

UV=UK

UV⎯⎯⎯⎯⎯⎯∥JL⎯⎯⎯⎯
(Correct answers are UW=1/2KL, UV---||JL---, JK=2VW)

Answer 1

The options 2,3 and 5 are correct.

Explanation:

From the figure it is noticed that the points U,V and W are midpoint of JK,KL and JL respectively.

Midpoints theorem of triangle states that the line connecting the midpoints of two sides is parallel to third side and its length is half of the third side.

The points U and W are midpoint of JK and JL. Using midpoint theorem, we get

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

`UW\parallel KL`

The points U and V are midpoint of JK and KL. Using midpoint theorem, we get

`UV=(1)/(2)JL`

`UV\parallel JL`

The points V and W are midpoint of KL and JL. Using midpoint theorem, we get

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

`2VW=JK`

`VW\parallel JK`

Therefore options 2, 3 and 5 are correct.