Question

The figure shows square KLMN. Which of the following conditions satisfy the criteria for squares?


Square KLMN with diagonals LN and KM


segment LK is congruent to segment LN

segment LM is parallel to segment LK

segment LM is parallel to segment LK

segment LM is parallel to segment KN

Answer 1

Answer:

First option: Square$KLMN$ with diagonals $LN$ and $KM$.

Fifth option: Segment $LM$is parallel to segment $KN$.

Step-by-step explanation:

We know that a square is quadriteral whose sides are equal.

By definition, a square has the following properties:

1) Its four sides are congruent.

2) The diagonals are congruent.

3) The angles formed by the intersection of the diagonals measure 90 degrees.

4) The opposite sides are parallel.

5) Each internal angle measures 90 degrees.

Notice in the figure that:

• The diagonals of the square  $KLMN$ are: $LN$ and $KM$.

• $LM$ and $KN$ are opposite sides, therefore, they are parallel.

Answer 2

Answer:

Segment LM is parallel to segment KN.

Step-by-step explanation:

In the given square KLMN with diagonals LN and KM, the correct condition which satisfy the given figure is option D, segment LM is parallel to segment KN.

The definition of a square is "a parallelogram which has all sides equal". And the definition of a parallelogram is "a four-side figure which opposite sides are parallel".

Therefore, if the square is a parallelogram, then its opposite sides are parallel and equal. From this deduction we have that segmenr LM is parallel and equal to segment KN, also segment LK is parallel and equal to MN.