if 2 of the line segments of a polygon are parallel, what is the least number of sides it could be?
Can you draw a 4-sided figure with 2 lines parallel ?
kaylah, you can't draw a triangle with 2 sides parallel !!
To determine the least number of sides of a polygon when two of its line segments are parallel, we need to consider the properties of polygons.
A polygon is a closed figure composed of straight sides called line segments. The number of sides in a polygon is equal to the number of angles.
To have a valid polygon, the sum of all its angles must be (n-2) * 180 degrees, where n is the number of sides.
When two line segments of a polygon are parallel, it creates a pair of opposite angles that are congruent (equal in measure). In a polygon, each angle is formed by two adjacent sides.
The only polygon where all the angles are congruent is a regular polygon. In regular polygons, all sides and angles are equal.
In a regular polygon, the sum of all the angles is (n-2) * 180 degrees. Since all the angles are congruent, dividing the sum of angles by the number of angles will give us the measure of each angle.
In a regular polygon with n sides, each angle measures (n-2) * 180 / n degrees.
If two angles are congruent, their measures are equal. So, we can set up an equation:
(n-2) * 180 / n = (n-2) * 180 / n
Cross-multiplying, we get:
(n-2) * n = (n-2) * 180
Expanding the equation:
n^2 - 2n = 180n - 360
Rearranging the terms:
n^2 - 182n + 360 = 0
Solving the quadratic equation, we find that n = 20 or n = 18.
Therefore, the least number of sides for a polygon with two parallel sides is 18.