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The perpendicular bisector of side KL of triangle KLM intersects side LN at point P. Complete the statement using one of the options given: If the perimeter of triangle KLM is 14 cm larger than the perimeter of triangle LMP, then...

Answer :

Final answer:

The perpendicular bisector of the side KL in triangle KLN intersects the side LN at point P, and the perimeter of KLN is greater than the perimeter of LMP.

Explanation:

The statement can be completed using the concept of perpendicular bisector of a side of a triangle. The perpendicular bisector of the side KL in triangle KLN intersects the side LN at point P. We can conclude that the perimeter of KLN is greater than the perimeter of LMP. To understand this, let's consider the properties of the perpendicular bisector. The perpendicular bisector of a side of a triangle is a line that divides the side into two equal halves and is perpendicular to that side. In this case, the perpendicular bisector of KL divides LN into two equal halves at point P. Since the perpendicular bisector is the line that is equidistant from the endpoints of the side, the length of LP is equal to the length of NP. Therefore, the length of LN is twice the length of LP.

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